How Technology Is Constantly Evolving And We Are Too With It

Technology is constantly evolving and we are too with it. We incorporate technology into our everyday lives to make them easier, provide entertain or be able to connect with one another. Arguably, no creation has made this more possible than Cyberspace. Prior to the twenty first century cyberspace was thought to be in the realm of science fiction, until a couple decades later technological breakthroughs brought it to existence. From that point on it has become essential to personal and global infrastructure. Storing our identity, personal information, wealth and for some our whole lives. Which makes it dangerous as well if abused. Cyberspace is a new frontier and we still don’t completely understand it. So how do we prosecute those who do harm to one another by means of cyberspace and cybercrime? Generally cybercrime branches of in to three major groups. Against a person, property or the government. A cybercrime against a person includes harassment and stalking a person through the internet/cyberspace. This is possible through the aids of email, social media and other sites or similar sorts. The types of harassment possible through cyberspace is sexual, racial, religious and others. Cybercrime against someone’s property include transmission of harmful programs and viruses. Also hacking corporate databases to steal information and money and email scams used to trick people to transfer money are all forms of cybercrime against property. The last and third major form ofShow MoreRelatedCause/Effect How Technology Influences Personal Relationships1095 Words   |  5 Pagesimpacts of digital technology on society. Technology has been evolving for hundreds of years. As it has become more advanced, the more it has taken a hold of the community. Digital technology is universal and there is no way to avoid it, but people need to start using it more responsibly. Everything gets taken for granted now that there are so many technological sources. Although there are a moderate amount of positive effects, the negative aspects outweigh them substantially. Technology use affects theRead MoreCan Technology Affect Your Mind?1607 Words   |  7 Pages1105 Emily Gilliam February 19, 2011 Can Technology affect your mind? iPod+ iPhone+ iPad= iBroke†Ã¢â‚¬ ¦and dysfunctional† Has your life begun to revolve around your cell phone? Are you checking your email, texting or tweeting more often than you speak to an actual human? Are you making life and death decisions at the computer. â€Å"Should I buy new iTunes or have gas for the rest of the week?† This is a growing problem. People have begun to let technology control their lives. They don’t have theRead MoreEssay on Nursing Informatics And Nursing889 Words   |  4 Pagesseen it in action many times. Are we as nurses changing with the times? What is nursing informatics? Why is it important to me? How do I rate on the nursing informatics knowledge scale? What is my plan to increase my knowledge base? These questions should be at the forefront of every nurse’s thoughts. The information age has come crashing down on us from every possible angle in our lives, it affects how we communicate, how we educate, how we socialize and how we raise our children. Thus, why wouldRead MorePositiv e And Negative Aspects Of Advertising1695 Words   |  7 Pagesconstant give and take from consumers. Furthermore, I have investigated certain technological benefits associated with advertising that improve effectiveness, and how advertising benefits consumers. On the contrary, I have evaluated some of the associated ethical issues, the promotion of unnecessary consumerism, psychological effects on learning, how younger generations are becoming less receptive, and the adverse affects on society as a whole. Regardless of the conflicting viewpoints it is best to be knowledgeableRead MoreAutomation In The Workforce. The Advancement Of Automation1435 Words   |  6 Pagesworkforce The advancement of automation has affected our everyday lives since the industrial revolution. Over the years we saw a drastic increase in unemployment due to the fact that machines and robots can now do the job more efficiently. Today we have adopted the idea of automation that we sometimes are unaware of the subtlety. We only become aware of the change when old technology advances or when there is a system malfunction while using the product. This monopoly is spreading through the workforceRead MoreGlobalization And The Global World1669 Words   |  7 PagesGlobalization is something that we see happening all around us. When we walk down the street it is impossible not to have an advertisement for major corporations like Nike, McDonalds, or Coca Cola flashing in front of your face. Everywhere our head turns, commercialism is there. It is unavoidable. The world around us is constantly developing, and that development begins with us. As the world keeps evolving, globalization is co nsidered inevitable. As humans, we naturally strive for success, seekingRead MoreMass Media Essay739 Words   |  3 Pagesduring the last century have literally changed our world and the way we get our information. These developments range from the telegraph, telephone, radio, television, and the Internet. All of which played a major role in not the way we receive information but also communicate. Instead of waiting days to get messages, we can now get them as they are happening. The following will discuss how each one has helped change the way that we receive our media and benefitted the American culture. The telegraphRead MorePrivacy Lost By David Holtzman1620 Words   |  7 Pagesnot be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized (US 1). It is important to understand the protection we do have under this law- even if it is very limited. This law was created to ensure that the government has limitations on its powers, and that it cannot gather any information from people without first asking the court for a warrant. Does this meanRead MoreA Battle Between Minds1064 Words   |  4 Pagesâ€Å"Right† and â€Å"wrong† are such ambiguous terms and can only be personally defined by an individual’s beliefs and values. It is said that our values are defined predominately by our upbringing, but what if it is more neurologically ingrained than we had perceived? Doctor Roger Wolcott Sperry, neurophysiologist, won the Nobel Pri ze in 1981 for his discoveries concerning the functional specialization of the cerebral hemispheres, in which he studied the cognitive effects caused by severing the longitudinalRead MorePrivacy Lost By David Holtzman1386 Words   |  6 Pagesnot be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized (US 1). It is important to understand the protection we do have under this law-even if it is very limited. This law was created to insure its citizens that the government has limitations on its powers, and that it cannot gather any information from people without first asking the court for a warrant. Does

Germany s Culture And Heritage - 1507 Words

Germany is a country in Western Europe, they are also wealthiest and most populated country in entire continent. Germany has the large amount of people in western Europe and also has the best economy system there. Germany’s landscapes are very similar to the United States, in Northern Germany that’s where you would find snowy mountains Mid-western would consist of the forested hills of the urbanized west. Even if Germany has a long history with everything from World War 2 and a lot of other events, the country is the youngest and newest even younger the United States. Germany. Before 1871 when Germany was called Prussia the land before was made up of many little kingdoms and Monarchies. This is why the Germans many consider themselves†¦show more content†¦Germany stayed but changed their name to Deutsches Reich which they had until the end of World War 2. In the 20th Century in Eastern Europe Germany was the most successful and powerful out of the European countries including Russia. They ended up crushing the Russians in the battle of Tannenberg. Russia was completely destroyed in all this and was forced to sign a peace treaty in March of 1918. Also during World War one the Germans made a ship that can be uses under water to surprise allies’ ships during the war. These boats where dubbed as German U boats by the allies, and are also known now as submarines today. In April of 1917 there was a cruise ship called the Lusitania which got shot up and sunk by a German -U-Boat forcing the United States of America into war against them. In September of 1919, this Austrian man by the name Adolf Hitler joined the politics. Adolf Hitler convinced people on the German committee that Germany was stabbed in the back by the Allies powers and the committee believed him and listened. They all came to the agreement that Germany was the best and was better than any country in the world and wanted all the Germans to live together to form a better, a greater Germany. The arty was racist and anti-Semitic which was understandable for the time being. In 1920 the small positions group was renamed the Nazi Party.Show MoreRelatedAdvantages And Disadvantages Of Tourism1661 Words   |  7 Pagesmoments among the time such as the beginning of the country in the medieval conquered by Romans, Mongolian and Chinese empires. In the 18’s century was influenced by the Latin countries as Italy, Spain and Portugal keeping even today the official language, the Latin. After the 19th century was overtook by Britain and Mussolini Italy follo wing a period of Germany domination in the time of the Second Great World War. The country won her independency in 1949 keeping strong relationship with the SovietRead MoreThe Importance of Archaeology1232 Words   |  5 Pagesis the study of historical and prehistorcial civilizations through the recovery and analysis of their materials culture. Moreover, it contains the study of human activity in the past. 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To attemptRead MoreUnesco And The World Heritage List1539 Words   |  7 PagesUNESCO and the World Heritage List After the devastation created by World War I, and II, UNESCO (United Nations Educational, Scientific, and Cultural Organization) was founded in 1945. This organization was created as a way to establish peace, based on humanity’s intellectual and moral solidarity. Then in 1972, UNESCO founded the World Heritage Convention as a way to protect sites of exceptional worldwide importance (UNESCO, 2012). This convention was later ratified by 191 countries, making itRead MoreReligious Transformations Of The United States1275 Words   |  6 Pagesreligious transformations. The following paragraphs will briefly examine five different transformations that have occurred during the history of religion in the United States. Pluralism is by definition, the coexistence of multiple, groups, religions, cultures, etc. One example of Pluralism that sticks out is the history of colonial Protestantism. As discussed in class, Protestantism stemmed from desire to reform the Roman Catholic Church. The actions of three figures, Martin Luther, John Calvin, and KingRead MoreCultural Background : A Cultural Perspective As A Future Counselor808 Words   |  4 Pagesfreckles definitely do not go unnoticed. â€Å"It’s the Irish in me,† I often respond, but if a person could look beyond my spotted skin to within, they’d see that I identify most with my German heritage. When my paternal grandparents immigrated from Germany to the United States in the 1950’s, they brought their culture with them, influencing future generations, and especially myself. After analyzing my three family generations, I was proud to learn how my cultural background has greatly contributed to my

Total Quality Management Proposal for Smart Pack Ltd.

Question: Discuss about the Total Quality Management Proposal for Smart Pack Ltd. Answer: Introduction Lego is a line of Plastic Construction toys and its flagship product, Lego, consists of colorful interlocking plastic bricks which could be connected and assembled in myriads of ways. The company has been using a strong, resilient material, ABS (Acrylonitrile butadiene styrene, since 1963 to manufacture its building pieces. In order to expand its business in Asian markets, the firm is looking for a subcontractor in Australia and for this it has approached a small niche manufacturer, Smart Pack Ltd. in Australia. The new manufacturer is expected to assemble small LEGO sets and manufacture toys that are highly compatible to Australian markets. But, prior to this the company needs to conduct a Total Quality Management process to be the most deserving subcontractor of Lego (ASQ Team, 2016). TQM basically describes the management approach to attain a long-term success by responding to the customer needs readily and satisfying them in every sense. The TQM approach asks all the participating employees of the company to work in the direction of improvement in the firms operations and introducing innovative ideas for reforming the workplace culture. A permanent climate is introduced under this process in which all the members of a company continuously improve their skills and capabilities to deliver the best services and high Quality products to its customers. There is a keen requirement of this assessment because Lego is a leading giant in the Toy industry and has been widely accepted over all the foreign markets just because of its commitment towards the quality of the products. The following Business report has been precisely written to highlight the core principles and techniques of the TQM process that are to be undertaken to produce the best outcomes to the parent company (Wiley, 2012). The report also deals with the precise implementation of the TQM approaches within the firm and for this even an action plan has been generated. The prime aim of this report is to convince the owner about the abilities of the Smart Pack Ltd. and why it should be readily considered as a sub-contractor in Australia over the other competitors in the markets. Core Principles of TQM In order to involve a great level of customer satisfaction, an organization needs to follow certain core principles: The organization should follow approaches and develop operations that are entirely customer focused and tends to deliver ultimate satisfaction to them. The tasks being done in order to improve the quality of services are only completed if they are readily accepted by the customers (Baumeyer, 2015). The employees should be promoted to be greatly involved in all the crucial decisions of the company. For this purpose, all types of restrictions should be removed from the workplace and the employees should be empowered with the power of decision making. Process centered thinking should become the utmost priority of the organization as the organization which considers efficiency of the processes over the outcomes is the ones that tend to be most successful (Hashmi, 2015). The Integrated system also forms a unique principle of the TQM. In integrated system all the participants knows about the vision and mission of the company and hence align all the perceptions and activities to achieve them. The plans that begin with a precise strategy have a high success rate. The Strategic and Systematic approach towards the attainment of goals gives a sound platform of effective service delivery to the customers. The approaches after implementation need a continuous improvement and adoption of new trends. The creative and innovative thinking has a capability to make the future decisions more efficient and effective. Decision making is an integral process in any organization but at the same time it is the responsibility of the executives to make this process fact-based instead of an abstract one. The fact-based decisions often allow the organization members to consider those decisions that are beneficial for all at the same time. Hence, with such an approach, the decision making process becomes an unbiased one (Scheid, 2010). Communication is the last but the most important principle of the TQM process. Effective communication tools allow the exact ideas and goals to be promoted among the participants of the organization. This also allows the executives to gain feedbacks of the subordinates over certain decisions and even increase their participation in the crucial aspects of the firm. Required Tools and Techniques There are a number of tools and techniques which are to be installed in order to achieve success while implementing the process elements of TQM. The Qualitative tools consist of subjective inputs which do not measure any numerical value, but give an abstract idea of something immeasurable. The other types of tools are quantitative ones which involve the analysis of the objective data and only consider something with which numerical value is attached (Presentationeze Team, 2016). The best known tools and techniques of a TQM include: The Flowcharts that could be efficiently used in examining activities or in brainstorming To identify the Cause and Effect processes, the researchers could implement the Fishbone or Ishikawa Diagrams. The primary categories are generally pre-determined in such cases (Jafari Setak, 2010). As the owner has already given a deadline of the submission of the business report to the subcontractor, hence, there could also be an implementation of Run Charts in which changes and data are plotted against timeline. As the TQM process highly focuses on improvement of the quality of services delivered to the customers, so a number of process improvement tools such as FMEA (Failure Mode Effects Analysis), PDCA (Plan Do Check Act), SIPOC Analysis and Statistical Control tools could also be included (Singh Grover, 2012). To efficiently implement and maintain the product and service quality, Smart Pack Ltd., being a small firm could also direct its resources in implementing the best TQM techniques of all time like Brainstorm Analysis, Fault Tree Analysis and Hazop Analysis (Gomes, 2011). Implementation of the TQM As Smart Pack Ltd. has to demonstrate its capabilities and abilities to Lego in order to be chosen as the best subcontractor in Australia above all the others, hence, it becomes its prime responsibility to give a candid description of what all will be included in the TQM process being carried out in the company. TQM approach demands a firm to deliver the best quality of goods and services to the customers and even satiate the needs of the workforce. TQM entirely talks about Quality and its improvement in the coming future and this definitely needs a precise plan that is to be communicated and followed by all the participants of the organization. As the company, Smart Pack Ltd. is planning to prove its capabilities in front of the owner as a potential subcontractor in Australia, so it needs to follow a certain set of steps that depicts the actual implementation of the TQM process in the entire organization. These steps are: Clarification of Mission, Vision and Values: The employees participating in the TQM process need to know where their talents and skills are being used and what exactly the vision of the firm is. When they are asked to deliver services that are goal-oriented, then their skills are utilized in a better manner. Orientation of the newly recruited employees is necessary to communicate the true values of the firm and its candid priorities while executing its operations. The Identification of CSF: CSF or the Critical Success Factors are to be identified in the initial stages of implementation of the TQM processes. This identification helps the executives to focus on those things that demands optimum resources, yet promises a huge success of the firm. Moreover, these performance-based factors also help in determining how well a company is performing and what all reformations are needed for the same. Identification of the Key Target Audiences and Customer Groups: Identification of the target groups is crucial prior to the development of products and services. The actual needs and demands of the customers help in framing customized services that have the potential in satiating all sorts of tastes and perceptions in the markets. The Key customer groups in this process include the Employees, the Customers, Vendors, Suppliers and other types of Volunteers that are highly influenced by the outcomes of the TQM process (Sharma, et al., 2014). Gathering Customer and Employee feedbacks: To evaluate the performance of the firm, the executives need to gather feedbacks from myriads of stakeholders. In the TQM processes these feedbacks could be gathered from the Customers and Employees. This will definitely increase their participation in the crucial decision making processes for the organization. Developing and Implementing Survey Tools: The Survey tools often help in identifying that what is best for the customers and in what manner, the organization could meet these requirements. The surveys often provide a starting point for the improvements and also demonstrate progress as improvement plans are implemented (Chandra, 2013). Planning and Implementing Improvement Plan: The customer feedbacks and survey tools help in gathering feedbacks over the current operations of the firm. After the baseline is established, the executives could develop and implement Improvement plans based on these feedbacks The Improvement Plans should have candid operations and should be accepted by all the participants of the organization. Monitoring the TQM process: Monitoring is important to ensure that there is consistent progress towards the goals. This process also helps the executives to determine what all resources have been used till now and what all are to be added for the smooth functioning of the company. Monitoring also helps in evaluating the change in priorities and objectives with the course of time to adapt to the ongoing trends in the business world. Considering the Technological Reformations: The technological elements are reforming at a rapid speed and the organization needs to keep pace with it. The TQM process could only be implemented in an effective manner if the executives consider all the leading changes at the technological level and implement those that could foster the success rates in the organization. Incorporate the achievements and Satisfaction data in the marketing plan: The Satisfaction experienced by the customers by the quality of the product and services of the firm could be used as a marketing tool to attract other customers in myriads of new markets. Similarly, the achievements of the company could also be showcased to gain the loyalty of the customers. Action Plan for the Implementation Below is the Action Plan for two years of implementation of the TQM process in Smart Pack Ltd. Tasks Strategies Person (s) responsible Resources needed Timeline 1. Communication of the exact mission, vision and values to all the stakeholders - Arrangement of weekly and monthly meetings - Effective Training and Interaction sessions - Leaders of the HR department - Experts hired from other organizations - Senior and middle managers - Efficient Conference rooms - Separate budget for meetings - Efficient network systems for upgraded online platforms (Lakhe Mohanty, 2014). - Within 1-2 months of the commencement of the TQM process. 2. Identification of the Critical Success Factors (CSF) - Considering the previous TQM activities occurred in the organization - Watching closely the trends during the success and downfall of the company - Financial manager with its team - Regulatory team with leaders from all the subunits of the organization. - Previous Annual reports and budgets - Reports on availability and lacking of resources within the company. - First Quarter of the first year of Implementation 3. Identification of Key Target Audiences and Customer groups - Launching sample products in the market to record the response and identify target consumers - Taking help from the local marketers to analyze the perceptions of consumers from different markets. - HR manager with the team - Leaders with efficient communication skills - Sample products - Local marketers reports - First two Quarters of the first year of implementation 4. Gathering Feedbacks - Surveys and Personal interviews - Asking customers to fill up the feedback forms. - Employees with interactive power - Company representatives to conduct surveys - Effective Survey Questions - Feedback forms and systems to process them (Floss, et al., 2012). The last quarter of the first year of implementation 5. Developing and Implementing Survey tools - Evaluating the texts for the best survey tools - Hiring experts from another firm to create effective survey questions - Leaders with good critically evaluation power - Representatives to conduct periodic checks and evaluation - The audit reports of the previous years - List of available survey tools in the company - Should begin from the third quarter of the first year of implementation 6. Planning and Implementing Improvement Plan - Design the layout of the best improvement plan - Compare the existing plans with that of the other leaders in the market - The team planning for improvements - Representatives of the company with intellect and innovation - Previous improvement plan - List of ongoing trends in the markets - A List of the improvements adopted by other companies - First quarter of the second year of implementation 7. Monitoring the TQM process -Regular Audits - Meetings - The Audit team - Leaders from all the subunits - The elements that would be undertaken under evaluation - Separate budget for hiring the monitoring team (Caro, 1983). - During the third and fourth quarter of the second year of implementation 8. Considering the Technological Reformations - Observing the current and future technological trends - The experts from the IT sector - Representatives with a command in IT field - Latest Technological tools and techniques - Throughout both the implementation year 9. Incorporation of the Achievements and Satisfaction data in the marketing plan - Recording periodically the success and satisfaction data - Leaders with critical evaluation abilities - Audit and Monitoring Reports - The last two quarters of the second year of implementation Recommendations and Conclusion The TQM process promises a great improvement in a firm and prepares it for a better future. To be the most desirable subcontractor, Smart Pack Ltd. should efficiently follow the above mentioned implementation steps in a given time frame and should even monitor the progress periodically. Moreover, as Lego is highly committed towards the quality of its products, hence, its subcontractor also has to consider the quality of the products and services above all the other operations in the company. References ASQ Team, 2016. What is Total Quality Management (TQM)?. What is Total Quality Management (TQM)?. Baumeyer, K., 2015. Five Principles of Total Quality Management (TQM). Five Principles of Total Quality Management (TQM). Caro, J. C., 1983. Planning and Implementing Total Quality Management (TQX) in a Naval service organization: A Case Study of Fleet Numerical oceanography Center: DTIC, Available at: https://www.dtic.mil/dtic/tr/fulltext/u2/a242311.pdf Chandra, P., 2013. A Study on Implementation of Total Quality Management in Businesses. International Journal of Engineering Science and Innovative Technology (IJESIT), May, 2(3), pp. 1-7. Floss, G., Lynch, T. Naughton, J., 2012. Total Quality Management Master Plan: GOAL/QPC Research Committee, Available at: https://www.goalqpc.com/cms/docs/tqmMasterPlan.pdf Gomes, S., 2011. Different techniques for TQM: Benchmarking: Wordpress, Available at: https://xisspm.files.wordpress.com/2011/07/chap-4-tqm-techniques.pdf Hashmi, K., 2015. Introduction and Implementation of Total Quality Management (TQM). Introduction and Implementation of Total Quality Management (TQM). Jafari, S. Setak, M., 2010. Total Quality Management Tools and Techniques: The Quest for an Implementation Roadmap. Total Quality Management Tools and Techniques: The Quest for an Implementation Roadmap. Lakhe, R. Mohanty, R., 2014. Total Quality Management Concepts, Evolution and Acceptability in Developing Economies, Available at: https://www.icesi.edu.co/blogs/bitacoraestrategia0314/files/2014/03/21-Total-Quality-Management-concepts.pdf Presentationeze Team, 2016. TQM Tools and Techniques. [Online] Available at: https://www.presentationeze.com/presentations/tqm-tools-and-techniques/ Scheid, J., 2010. Analysis of TQM Quality Concepts. Analysis of TQM Quality Concepts, 16 December. Sharma, S., Gupta, S. Singh, R., 2014. Implementation Of TQM For Improving Organizational Effectiveness. International Journal of Application or Innovation in Engineering Management, September.3(9). Singh, M. Grover, S., 2012. Tools and techniques for quality management in manufacturing industries: YMCA University of Science Technology, Available at: https://ymcaust.ac.in/tame2012/cd/industrial/IE-30.pdf Wiley, 2012. Total Quality Management. In: Total Quality Management, pp. 1-35, Available at: https://www.wiley.com/college/sc/reid/chap5.pdf

Matrices in Matlab Essay Example

Matrices in Matlab Paper Matrices in Matlab You can think of a matrix as being made up of 1 or more row vectors of equal length. Equivalently, you can think of a matrix of being made up of 1 or more column vectors of equal length. Consider, for example, the matrix ? ? 1 2 3 0 A = ? 5 ? 1 0 0 ? . 3 ? 2 5 0 One could say that the matrix A is made up of 3 rows of length 4. Equivalently, one could say that matrix A is made up of 4 columns of length 3. In either model, we have 3 rows and 4 columns. We will say that the dimensions of the matrix are 3-by-4, sometimes written 3 ? . We already know how to enter a matrix in Matlab: delimit each item in a row with a space or comma, and start a new row by ending a row with a semicolon. gt;gt; A=[1 2 3 0;5 -1 0 0;3 -2 5 0] A = 1 2 3 0 5 -1 0 0 3 -2 5 0 We can use Matlab’s size command to determine the dimensions of any matrix. gt;gt; size(A) ans = 3 4 That’s 3 rows and 4 columns! Indexing Indexing matrices in Matlab is similar to the indexing we saw with ve ctors. The di? erence is that there is another dimension 2. To access the element in row 2 column 3 of matrix A, enter this command. 1 2Copyrighted material. See: http://msenux. redwoods. edu/Math4Textbook/ We’ll see later that we can have more than two dimensions. 76 Chapter 2 Vectors and Matrices in Matlab gt;gt; A(2,3) ans = 0 This is indeed the element in row 2, column 3 of matrix A. You can access an entire row with Matlab’s colon operator. The command A(2,:) essentially means â€Å"row 2 every column† of matrix A. gt;gt; A(2,:) ans = 5 -1 0 0 Note that this is the second row of matrix A. Similarly, you can access any column of matrix A. The notation A(:,2) is pronounced â€Å"every row column 2† of matrix A. gt;gt; A(:,2) ans = 2 -1 -2 Note that this is the second column of matrix A. You can also extract a submatrix from the matrix A with indexing. Suppose, for example, that you would like to extract a submatrix using rows 1 and 3 and columns 2 and 4. gt;gt; A([1,3],[2,4]) ans = 2 0 -2 0 Study this carefully and determine if we’ve truly selected rows 1 and 3 and columns 2 and 4 of matrix A. It might help to repeat the contents of matrix A. Section 2. 2 Matrices in Matlab 77 gt;gt; A A = 1 5 3 2 -1 -2 3 0 5 0 0 0 You can assign a new value to an entry of matrix A. gt;gt; A(3,4)=12 A = 1 2 5 -1 3 -2 3 0 5 0 0 12 When you assign to a row, column, or submatrix of matrix A, you must replace the contents with a row, column, or submatrix of equal dimension. For example, this next command will assign new contents to the ? rst row of matrix A. gt;gt; A(1,:)=20:23 A = 20 21 22 5 -1 0 3 -2 5 23 0 12 There is an exception to this rule. If the right side contains a single number, then that number will be assigned to every entry of the submatrix on the left. For example, to make every entry in column 2 of matrix A equal to 11, try the following code. gt;gt; A(:,2)=11 A = 20 11 5 11 3 11 22 0 5 23 0 12 It’s interesting what hap pens (and very powerful) when you try to assign a value to an entry that has a row or column index larger than the corresponding dimension of the matrix. For example, try this command. 78 Chapter 2 Vectors and Matrices in Matlab gt;gt; A(5,5)=777 A = 20 11 5 11 3 11 0 0 0 0 22 0 5 0 0 23 0 12 0 0 0 0 0 0 777 Note that Matlab happily assigns 777 to row 5, column 5, expanding the dimensions of the matrix and padding the missing entries with zeros. gt;gt; size(A) ans = 5 5 The Transpose of a MatrixYou can take the transpose of a matrix in exactly the same way that you took the transpose of a row or column vector. For example, form a â€Å"magic† matrix with the following command. gt;gt; A=magic(4) A = 16 2 5 11 9 7 4 14 3 10 6 15 13 8 12 1 You can compute AT with the following command. gt;gt; A. ’ ans = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 Section 2. 2 Matrices in Matlab 79 Note that the ? rst row of matrix AT was previously the ? rst column of matrix A. The second row of matrix AT was previously the second column of matrix A, and so on for the third and fourth columns of matrix AT . In essence, taking the transpose re? cts the matrix A across its main diagonal (upper left corner to lower right corner), so the rows of A become columns of AT and the columns of A become rows of AT . Building Matrices Matlab has some powerful capabilities for building new matrices out of one or more matrices and/or vectors. For example, start by building a 2 ? 3 matrix of ones. gt;gt; A=ones(2,3) A = 1 1 1 1 1 1 Now, build a new matrix with A as the ? rst column and A as the second column. As we are not starting a new row, we can use either space or commas to delimit the row entries. gt;gt; C=[A A] C = 1 1 1 1 1 1 1 1 1 1 1 1On the other hand, suppose that we want to build a new matrix with A as the ? rst row and A as the second row. To start a new row we must end the ? rst row with a semicolon. gt;gt; C=[A; A] C = 1 1 1 1 1 1 1 1 1 1 1 1 Let’s create a 2 ? 3 matrix of all zeros. 80 Chapter 2 Vectors and Matrices in Matlab gt;gt; D=zeros(2,3) D = 0 0 0 0 0 0 Now, let’s build a matrix out of the matrices A and D. gt;gt; E=[A D;D A] E = 1 1 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 1 The possibilities are endless, with one caveat. The dimensions must be correct or Matlab will report an error. For example, create a 2 ? 2 matrix of ones. gt;gt; A=ones(2,2) A = 1 1 1 1 And a 2 ? 3 matrix of zeros. gt;gt; B=zeros(2,3) B = 0 0 0 0 0 0 It’s possible to build a new matrix with A and B as row elements. gt;gt; C=[A B] C = 1 1 1 1 0 0 0 0 0 0 Section 2. 2 Matrices in Matlab 81 But it’s not possible to build a new matrix with A and B as column elements. gt;gt; C=[A;B] Error using ==gt; vertcat CAT arguments dimensions are not consistent. This happens because A has 2 columns, but B has 3 columns, so the columns don’t line up. We’ll see in later work that the matrix building capabilities of Matlab are a powerful ally . Scalar-Matrix MultiplicationIf asked to multiply a matrix by a scalar, one would hope that the operation of scalar-matrix multiplication would be carried out in exactly the same manner as scalar-vector multiplication. That is, simply multiply each entry of the matrix by the scalar. Example 1. If A is the matrix ? 1 2 3 A = 3? 4 5 6? , 7 8 9 ? perform the scalar-matrix multiplication 3A. Simply multiply 3 times each ? 1 3A = 3 ? 4 7 entry of the matrix. ? ? ? 2 3 3 6 9 5 6 ? = ? 12 15 18 ? 8 9 21 24 27 Matlab understands scalar-matrix multiplication. First, enter matrix A. gt;gt; A=[1 2 3;4 5 6;7 8 9] A = 1 2 3 4 5 6 7 8 9 Now compute 3A. 82 Chapter 2Vectors and Matrices in Matlab gt;gt; 3*A ans = 3 12 21 6 15 24 9 18 27 Matrix Addition If two matrices have the same dimension, then add the matrices by adding the corresponding entries in each matrix. Example 2. If A and B are the matrices ? ? ? ? 1 1 1 1 1 1 A = ? 2 2 2? and B = ? 1 1 1? , 3 3 3 1 1 1 ? nd the sum A + B. Simply add the corresponding entries. ? ? ? ? ? ? 1 1 1 1 1 1 2 2 2 A + B = ? 2 2 2? + ? 1 1 1? = ? 3 3 3?. 3 3 3 1 1 1 4 4 4 Matlab understands matrix addition. gt;gt; A=[1 1 1;2 2 2;3 3 3]; B=[1 1 1;1 1 1;1 1 1]; gt;gt; A+B ans = 2 2 2 3 3 3 4 4 4 This is identical to the hand-calculated sum above.Let’s look what happens when the dimensions are not the same. Example 3. If A and B are the matrices Section 2. 2 ? 1 1 1 A = ? 2 2 2? 3 3 3 ? then ? nd the sum A + B. Note the dimensions of each matrix. Matrices in Matlab 83 and B= 1 1 1 , 1 1 1 gt;gt; A=[1 1 1;2 2 2;3 3 3]; B=[1 1 1;1 1 1]; gt;gt; size(A) ans = 3 3 gt;gt; size(B) ans = 2 3 The matrices A and B do not have the same dimensions. Therfore, it is not possible to sum the two matrices. gt;gt; A+B Error using ==gt; plus Matrix dimensions must agree. This error message is completely expected. One ? nal example is in order. Example 4. If matrix A is ? 1 1 1 A = ? 2 2 2? 3 3 3 compute A + 1. Note that this addition of a matrix and a scalar makes no sense. ? ? 1 1 1 A + 1 = ? 2 2 2? + 1 3 3 3 ? 84 Chapter 2 Vectors and Matrices in Matlab The dimensions are all wrong. However, this is such a common occurrence in algebraic calculations (as we will see throughout the course), Matlab allows this matrix-scalar addition. gt;gt; A=[1 1 1;2 2 2;3 3 3]; gt;gt; A+1 ans = 2 2 2 3 3 3 4 4 4 Matlab simply adds 1 to each entry of the matrix A. That is, Matlab interprets A + 1 as if it were the matrix addition of Example 2. Matrix addition enjoys several properties, which we will ask you to explore in the exercises. . Addition is commutative. That is, A + B = B + A for all matrices A and B having the same dimension. 2. Addition is associative. That is, (A + B) + C = A + (B + C), for all matrices A, B, and C having the same dimension. 3. The zero matrix is the additive identity. That is, if A is m ? n and 0 is an m ? n matrix of all zeros, then A + 0 = A. 4. Each matrix A has an additive inverse. Form the matrix ? A by negatin g each entry of the matrix A. Then, A + (? A) = 0. Matrix-Vector Multiplication Consider the linear system of three equations in three unknowns. 2x + 3y + 4z = 6 3x + 2y + 4z = 8 5x ? 3y + 8x = 1. 2. 1) Because each of the corresponding entries are equal, the following 3 ? 1 vectors are also equal. ? ? ? ? 2x + 3y + 4z 6 ? 3x + 2y + 4z ? = ? 8 ? 5x ? 3y + 8x 1 Section 2. 2 Matrices in Matlab 85 The left-hand vector can be written as a vector sum. ? ? ? ? ? ? ? ? 2x 3y 4z 6 ? 3x ? + ? 2y ? + ? 4z ? = ? 8 ? 5x ? 3y 8z 1 Scalar multiplication can be used to factor the variable out of each vector on the left-hand side. ? ? ? ? ? ? ? ? 2 3 4 6 x? 3? + y? 2 ? + z? 4? = ? 8? (2. 2) 5 ? 3 8 1 The construct on the left-hand side of this result is so important that we will pause to make a de? nition.Definition 5. Let ? 1 , ? 2 , . . . , and ? n be scalars and let v1 , v2 , . . . , and vn be vectors. Then the construction ? 1 v1 + ? 2 v2 +  ·  ·  · + ? n vn is called a linear combination of the vectors v1 , v2 , . . . , and vn . The scalars ? 1 , ? 2 , . . . , and ? n are called the weights of the linear combination. For example, we say that ? ? ? ? ? ? 2 3 4 ? 3? + y? 2 ? + z? 4? x 5 ? 3 8 is a linear combination of the vectors [2, 3, 5]T , [3, 2, ? 3]T , and [4, 4, 8]T . 3 Finally, we take one last additional step and write the system (2. 2) in the form ? ? ? ? 2 3 4 x 6 ? 3 2 4 y ? = ? 8?. (2. 3) 5 ? 8 z 1 Note that the system (2. 3) has the form Ax = b, where 3 Here we use the transpose operator to save a bit of space in the document. 86 Chapter 2 ? Vectors and Matrices in Matlab ? ? x ? y ? , x= z ? ? 6 ? 8?. b= 1 ? 2 3 4 A = ? 3 2 4? , 5 ? 3 8 and The matrix A in (2. 3) is called the coe? cient matrix. If you compare the coe? cient matrix in (2. 3) with the original system (2. 1), you see that the entries of the coe? cient matrix are simply the coe? cients of x, y, and z in (2. 1). On right-hand side of system (2. 3), the vector b = [6, 8, 1]T contains the n umbers on the right-hand side of the original system (2. ). Thus, it is a simple matter to transform a system of equations into a matrix equation. However, it is even more important to compare the left-hand sides of system (2. 2) and system (2. 3), noting that ? ? ? ? ? ? ? ? 2 3 4 x 2 3 4 ? 3 2 4 y ? = x? 3? + y? 2 ? + z? 4?. 5 ? 3 8 z 5 ? 3 8 This tells us how to multiply a matrix and a vector. One takes a linear combination of the columns of the matrix, using the entries in the vector as weights for the linear combination. Let’s look at an example of matrix-vector multiplication Example 6. Multiply the matrix and vector ? ? 1 2 ? 3 1 ? 3 0 4 ? ? ? 2 ? . 0 ? 2 3 To perform the multiplication, take a linear combination of the columns of the matrix, using the entries in the vector as weights. ? ? ? ? ? ? ? ? 1 2 ? 3 1 1 2 ? 3 ? 3 0 4 ? ? ? 2 ? = 1 ? 3 ? ? 2 ? 0 ? + 3 ? 4 ? 0 ? 2 2 3 0 ? 2 2 ? ? ? ? ? ? 1 ? 4 ? 9 ? 3 ? + ? 0 ? + ? 12 ? = 0 4 6 ? ? ? 12 ? 15 ? = 10 Itâ€℠¢s important to note that this answer has the same number of entries as does each column of the matrix. Section 2. 2 Matrices in Matlab 87 Let’s see if Matlab understands this form of matrix-vector multiplication. First, load the matrix and the vector. gt;gt; A=[1 2 -3;3 0 4;0 -2 2]; x=[1; -2; 3]; Now perform the multiplication. gt;gt; A*x ans = -12 15 10 Note this is identical to our hand calculated result. Let’s look at another example. Example 7. Multiply Ax, where A= 1 1 1 2 0 ? 2 and x = 1 . 1 If you try to perform the matrix-vector by taking a linear combination using the entries of the vectors as weights, Ax = 1 1 1 2 0 ? 2 1 1 1 1 =1 +1 +? . 1 2 0 ? 2 (2. 4) The problem is clear. There are not enough weights in the vector to perform the linear combination. Let’s see if Matlab understands this â€Å"weighty† problem. gt;gt; A=[1 1 1;2 0 -2]; x=[1; 1]; gt;gt; A*x Error using ==gt; mtimes Inner matrix dimensions must agree.Inner dimensions? Let†™s see if we can intuit what that means. In our example, matrix A has dimensions 2 ? 3 and vector x has dimensions 2 ? 1. If we juxtapose these dimensions in the form (2? 3)(2? 1), then the inner dimensions don’t match. 88 Chapter 2 Vectors and Matrices in Matlab Dimension Requirement. If matrix A has dimensions m ? n and vector x has dimensions n ? 1, then we say â€Å"the innner dimensions match,† and the matrix-vector product Ax is possible. In words, the number of columns of matrix A must equal the number of rows of vector x. Matrix-Matrix Multiplication We would like to extend our de? ition of matrix-vector multiplication in order to ? nd the product of matrices. Here is the needed de? nition. Definition 8. Let A and B be matrices and let b1 , b2 , . . . , and bn represent the columns of matrix B. Then, AB = A b1 , b2 , . . . , bn = Ab1 , Ab2 , . . . , Abn . Thus, to take the product of matrices A and B, simply multiply matrix A times each vector column of matri x B. Let’s look at an example. Example 9. Multiply 1 2 3 4 1 ? 2 . 2 1 We multiply the ? rst matrix times each column of the second matrix, then use linear combinations to perform the matrix-vector multiplications. 1 2 3 4 1 ? = 2 1 = 1 = 1 2 3 4 1 , 2 1 2 3 4 ? 2 1 1 2 1 2 +2 , ? 2 +1 3 4 3 4 5 0 11 ? 2 Let’s see if Matlab understands this form of matrix-matrix multiplication. First, load the matrices A and B. gt;gt; A=[1 2;3 4]; B=[1 -2;2 1]; Now, multiply. Section 2. 2 Matrices in Matlab 89 gt;gt; A*B ans = 5 11 0 -2 Note that this result is indentical to our hand calculation. Again, the inner dimensions must match or the matrix-matrix multiplication is not possible. Let’s look at an example where things go wrong. Example 10. Multiply 1 1 1 2 0 ? 2 1 2 . 3 4 When we multiply the ? rst matrix times each column of the second matrix, we immediately see di? ulty with the dimensions. 1 1 1 2 0 ? 2 1 2 = 3 4 1 1 1 2 0 ? 2 1 , 3 1 1 1 2 0 ? 2 2 4 (2. 5) In the ? rst column of the matrix product, the matrix-vector multiplication is not possible. The number of columns of the matrix does not match the number of entries in the vector. Therefore, it is not possible to form the product of these two matrices. Let’s see if Matlab understands this dimension di? culty. gt;gt; A=[1 1 1;2 0 -2]; B=[1 2;3 4]; gt;gt; A*B Error using ==gt; mtimes Inner matrix dimensions must agree. The error message is precisely the one we would expect. Dimension Requirement.If matrix A has dimensions m ? n and matrix B has dimensions n ? p, then we say â€Å"the inner dimensions match,† and the matrix-matrix product AB is possible. In words, the number of columns of matrix A must equal the number of rows of matrix B. Let’s look at another example. 90 Chapter 2 Vectors and Matrices in Matlab Example 11. Multiply ? 1 2 1 1 1 ? AB = 1 ? 2 ? . 2 0 ? 2 2 0 Load the matrices A nd B into Matlab and check their dimensions. gt;gt; A=[1 1 1;2 0 -2]; B=[1 2;1 -2; 2 0]; gt;gt; size(A) ans = 2 3 gt;gt; size(B) ans = 3 2 Thus, matrix A has dimensions 2 ? 3 and B has dimensions 3 ? . Therefore, the inner dimensions match (they both equal 3) and it is possible to form the product of A and B. gt;gt; C=A*B C = 4 -2 ? 0 4 Note the dimensions of the answer. gt;gt; size(C) ans = 2 2 Recall that A was 2 ? 3 and B was 3 ? 2. Note that the â€Å"outer dimensions† are 2 ? 2, which give the dimensions of the product. Dimensions of the Product. If matrix A is m ? n and matrix B is n ? p, then the dimensions of AB will be m ? p. We say that the â€Å"outer dimensions give the dimension of the product. † Section 2. 2 Matrices in Matlab 91 Properties of Matrix MultiplicationMatrix multiplication is associative. That is, for any matrices A, B, and C, providing the dimensions are right, (AB)C = A(BC). Let’s look at an example. Example 12. Given A= 2 2 , 3 3 B= 1 1 , 2 5 and C = 3 3 , 2 5 use Matlab to demonstrate that (AB)C = A(BC). Load the matrices A, B, and C into Matlab, then calculate the left-hand side of (AB)C = A(BC). gt;gt; A=[2 2;3 3]; B=[1 1;2 5]; C=[3 3;2 5]; gt;gt; (A*B)*C ans = 42 78 63 117 Next, calculate the right-hand side of (AB)C = A(BC). gt;gt; A*(B*C) ans = 42 78 63 117 Hence, (AB)C = A(BC). Matrix Multiplication is Associative.In general, if A, B, and C have dimensions so that the multiplications are possible, matrix multiplication is associative. That is, it is always the case that (AB)C = A(BC). 92 Chapter 2 Vectors and Matrices in Matlab Unfortunately, matrix multiplication is not commutative. That is, even if A and B are of correct dimensions, it is possible that AB = BA. Let’s look at an example. Example 13. Let A= 1 2 3 4 and B = 3 5 . 2 7 Do the matrices A and B commute? That is, does AB = BA? Load the matrices into Matlab, then compute AB. gt;gt; A=[1 2;3 4]; B=[3 5;2 7]; gt;gt; A*B ans = 7 19 17 43 Now compute BA. gt;gt; B*A ans = 18 23 6 32 Thus, AB = BA. Matrix Multiplication is not Commutative. In general, even if the dimensions of A and B allow us to reverse the order of multiplication, matrices A and B will not commute. That is, AB = BA. Any change in the order of multiplication of matrices will probably change the answer. Some matrices do commute, making this even more complicated. Section 2. 2 Matrices in Matlab 93 gt;gt; A=[5 3;7 4],B=[-4 3;7 -5]; gt;gt; A*B ans = 1 0 0 1 gt;gt; B*A ans = 1 0 0 1 In this case, AB = BA. However, in general, matrix multiplication is not commutative. The loss of the commutative property is not to be taken lightly.Any time you change the order of multiplication, you are risking an incorrect answer. There are many insidious ways that changes of order can creep into our calculations. For example, if you multiply the left-hand side of equation on the left by a matrix A, then multiply the right-hand side of the equation on the right by the same matrix A, you’ve changed the order and should expect an incorrect answer. W e will explore how the loss of the commutative property can adversely a? ect other familiar algebraic properties in the exercises. Here is a list of matrix properties you can depend on working all of the time.Let A and B be matrices of the correct dimension so that the additions and multiplications that follow are possible. Let ? and ? be scalars. A(B + C) = AB + AC (A + B)C = AC + BC. (? + ? )A = ? A + ? A ? (A + B) = ? A + ? B. ?(? A) = ( )A. (? A)B = ?(AB) = A(? B). For example, as stated above, matrix multiplication is distributive over addition. That is, A(B + C) = AB + AC. gt;gt; A=[2 3;-1 4]; B=[1 2;0 9]; C=[-3 2;4 4]; gt;gt; A*(B+C) ans = 8 47 18 48 gt;gt; A*B+A*C ans = 8 47 18 48 94 Chapter 2 Vectors and Matrices in Matlab We will explore the remaining properties in the exercises. Section 2. 2 Matrices in Matlab 95 2. Exercises 1. Given the matrices A= and C= 3 1 , 5 8 3 3 , 2 1 B= 1 1 , 2 3 and C= 1 2 , 0 9 3. Given the matrices A= 1 0 , 2 5 B= 0 1 , 2 7 use Matlab to veri fy each of the following properties. Note that 0 represents the zero matrix. a) A + B = B + A b) (A + B) + C = A + (B + C) c) A + 0 = A d) A + (? A) = 0 use Matlab to verify each of the following forms of the distributive property. a) A(B + C) = AB + AC b) (A + B)C = AC + BC 4. Given the matrices A= 2 2 , 4 7 B= 3 1 , 8 9 2. The fact that matrix multiplication is not commutative is a huge loss. For example, with real numbers, the following familiar algeraic properties hold. . = ii. (a + b)2 = a2 + 2ab + b2 iii. (a + b)(a ? b) = a2 ? b2 Use Matlab and the matrices A= 1 1 4 2 and B = 2 3 1 6 (ab)2 a2 b2 and the scalars ? = 2 and ? = ? 3, use Matlab to verify each of the following properties. a) (? + ? )A = ? A + ? A b) ? (A + B) = ? A + ? B c) ? (? A) = ( )A d) (? A)B = ? (AB) = A(? B) 5. Enter the matrices A=pascal(3) and B=magic(3). a) Use Matlab to compute (A+B)T . b) Use Matlab to compute AT + B T and compare your result with the result from part (a). Explain what your learned in this exercise. to show that none of these properties is valid for these choices of A and B.Can you explain why each of properties (i-iii) is not valid for matrix multiplication? Hint: Try to expand the left-hand side of each property to arrive at the right-hand side. 96 Chapter 2 Vectors and Matrices in Matlab a) What is the result of the Matlab command A(:,2)=[ ]? Note: [ ] is the empty matrix. b) Refresh matrix A with A=pascal(4). What is the result of the Matlab command A(3,:)=[ ]? 13. Enter the matrix A=pascal(5). a) What command will add a row of all ones to the bottom of matrix A? Use Matlab to verify your conjecture. b) What command will add a column of all ones to the right end of matrix A?Use Matlab to verify your conjecture. 14. Enter the matrix A=magic(3). Execute the command A(5,4)=0. Explain the resulting matrix. 15. Enter the matrix A=ones(5). a) Explain how you can insert a row of all 5’s betwen rows 2 and 3 of matrix A. Use Matlab to verify your conjecure. b) Explain how you can insert a column of all 5’s betwen columns 3 and 4 of matrix A. Use Matlab to verify your conjecure. 16. Enter the matrix ? ? 1 2 3 A = ? 4 5 6?. 7 8 9 a) What is the output of the Matlab command A=A([1,3,2],:)? 6. Enter the matrix A=pascal(4) and the scalar ? = 5. a) Use Matlab to compute (? A)T . b) Use Matlab to compute ?A and compare your result with the result from part (a). Explain what your learned in this exercise. 7. Using hand calculations only, calculate the following matrix-vector product, then verify your result in Matlab. ? ? 1 1 2 1 ? 3 4 0 2 ? 0 5 6 ? 5 8. Write the following system of linear equations in matrix-vector form. 2x + 2y + 3z = ? 3 4x + 2y ? 8z = 12 3x + 2y + 5z = 10 9. Using hand calculations only, calculate the following matrix-matrix product, then verify your result in Matlab. ? ? 2 3 1 1 1 4 ? 0 1 2 0 0 5? 0 0 5 3 5 2 10. Enter the matrix magic(8). What Matlab command will zero out all of the even rows?Use Matlab to verify your conjecture. 11. Enter the matrix pascal(8). What Matlab command will zero out all of the odd columns? Use Matlab to verify your conjecture. 12. Enter the matrix A=pascal(4). Section 2. 2 b) Refresh matrix A to its original value. What Matlab command will swap columns 1 and 3 of matrix A? Use Matlab to verify your conjecture. 17. Enter the matrix ? ? 1 2 3 A = ? 4 5 6?. 7 8 9 a) Enter the Matlab command A(2,:)=A(2,:)-4*A(1,:)? Explain the result of this command. b) Continue with the resulting matrix A from part (a). What is the output of the Matlab command A(3,:)=A(3,:)-7*A(1,:)?Explain the result of this command. 18. Type format rat to change the display to rational format. Create a 3 ? 3 Hilbert matrix with the command H=hilb(3). a) What is the output of the Matlab command H(1,:)=6*H(:,1)? Explain the result of this command. b) Continue with the resulting matrix H from part (a). What command will clear the fractions from row 2 of this result? 19. Enter the matrices A=magic(3) and B=pascal(3). Execute the command C=A+i*B. Note: You may have to enter clear i to return i to its default (the square root of ? 1). a) What is the transpose of the matrix C? Use Matlab to verify your Matrices in Matlab 97 esponse. b) What is the conjugate transpose of the matrix C? Use Matlab to verify your response. 20. Use Matlab’s hadamard(n) command to form Hadarmard matrices of order n = 2, 4, 8, and 16. In each case, use Matlab to calculate H T H. Note the pattern. Explain in your own words what would happen if your formed the matrix product H T H, where H is a Hadamard matrix of order 256. 21. Enter the Matlab command magic(n) to form a â€Å"magic† matrix of order n = 8. Use Matlab’s sum command to sum both the columns and the rows of your â€Å"magic† matrix. Type help sum to learn how to use the syntax sum(X,dim) to accomplish this goal.What is â€Å"magic† about this matrix? 22. Enter the Matlab command A=magic(n) to form a â€Å"mag ic† matrix of order n = 8. Use Matlab’s sum command to sum the columns of your â€Å"magic† matrix. Explain how you can use matrix-vector multilication to sum the columns of matrix A. 23. Set A=pascal(5) and then set I=eye(5), then ? nd the matrix product AI. Why is I called the identity matrix? Describe what a 256 ? 256 identity matrix would look like. 24. Set A=pascal(4) and then set B=magic(4). What operation will produce the second column of the matrix product AB? Can this be done 98 Chapter 2 Vectors and Matrices in Matlab 28.Enter the Matlab command hankel(x) to form a Hankel matrix H, where x is the vector [1, 2, 3, 4]. The help ? le for the hankel commands describes the Hankel matrix as a symmetric matrix. Take the transpose of H. Describe what is mean by a symmetric matrix. 29. A Hilbert matrix H is de? ned by H(i, j) = 1/(i + j ? 1), where i ranges from 1 to the number of rows and j ranges from 1 to the number of columns. Use this de? nition and hand ca lculations to ? nd a Hilbert matrix of dimension 4 ? 4. Use format rat and Matlab’s hilb command to check your result. 30. The number of ways to choose k objects from a set of n objects is de? ed and calcualted with the formula n k = n! . k! (n ? k)! without ? nding the product AB? 25. Set the vector v=(1:5). ’ and the vector w=(2:6). ’. a) The product vT w is called an inner product because of the position of the transpose operator. Use Matalb to compute the inner product of the vectors v and w. b) The product vwT is called an outer product because of the position of the transpose operator. Use Matalb to compute the outer product of the vectors v and w. 26. Enter A=[0. 2 0. 6;0. 8 0. 4]. Calculate An for n = 2, 3, 4, 5, etc. Does this sequence of matrices converge? If so, to what approximate matrix do they converge? 7. Use Matlab ones command to create the matrices ? ? 2 2 2 1 1 A= , B = ? 2 2 2? , 1 1 2 2 2 and 3 3 . 3 3 Craft a Matlab command that will build the block diagonal matrix ? ? A 0 0 C = ? 0 B 0 ? , 0 0 C where the zeros in this matrix represent matrices of zeros of the appropriate size. De? ne a Pascal matrix P with the formula P (i, j) = i+j? 2 , i? 1 where i ranges from 1 to the number of rows and j ranges from 1 to the number of columns. Use this de? nition and hand calculations to ? nd a Pascal matrix of dimension 4 ? 4. Use Matlab’s pascal command to check your result. Section 2. 2 Matrices in Matlab 99 2. 2 Answers 1. ) Enter the matrices. gt;gt; A=[3 3;2 1]; B=[1 1;2 3]; Calculate A + B. gt;gt; A+B ans = 4 4 gt;gt; A+(B+C) ans = 7 5 9 12 c) Enter the matrix A and the zero matrix. gt;gt; A=[3 3;2 1]; O=zeros(2,2); 4 4 Calculate A + 0. gt;gt; A+O ans = 3 2 Calculate A. gt;gt; A A = 3 2 3 1 Calculate B + A. gt;gt; B+A ans = 4 4 3 1 4 4 b) Enter the matrices gt;gt; A=[3 3;2 1]; B=[1 1;2 3]; gt;gt; C=[3 1;5 8]; Calculate (A + B)C. gt;gt; (A+B)+C ans = 7 5 9 12 Calculate AC + BC. d) Enter the matrix A and the zero mat rix. startMatlab gt;gt; A=[3 3;2 1]; O=zeros(2,2); Calculate A + (? A). 100 Chapter 2 Vectors and Matrices in Matlab gt;gt; A+(-A) ans = 0 0 0 0 Calculate the zero matrix. gt;gt; O O = 0 0 0 0 5. gt;gt; (A+B)*C ans = 1 11 4 116 gt;gt; A*C+B*C ans = 1 11 4 116 a) Ener the matrices A and B. gt;gt; A=pascal(3); B=magic(3); Compute (A + B)T . 3. a) Enter the matrices A, B, and C. gt;gt; A=[1 0;2 5]; B=[0 1;2 7]; gt;gt; C=[1 2;0 9]; Compare A(B + C) and AB + AC. gt;gt; A*(B+C) ans = 1 3 12 86 gt;gt; A*B+A*C ans = 1 3 12 86 b) Enter the matrices A, B, and C. gt;gt; A=[1 0;2 5]; B=[0 1;2 7]; gt;gt; C=[1 2;0 9]; Compare (A+B)C and AC +BC. gt;gt; (A+B). ’ ans = 9 4 2 7 7 10 b) Compute AT + B T . gt;gt; A. ’+B. ’ ans = 9 4 2 7 7 10 12 8 5 12 8 The transpose of the sum of two matrices is equal to the sum of the transposes of the two matrices. 7. Enter matrix A and vector x. Section 2. 2 13. gt;gt; A=[1 1 2;3 4 0;0 5 6]; gt;gt; x=[1 2 5]. ’; Calculate Ax. gt;gt; A*x ans = 13 11 40 Matrices in Matlab 101 a) Enter the matrix A. gt;gt; A=pascal(5) To add a row of all ones to the bottom of the matrix, execute the following command. gt;gt; A(6,:)=ones(5,1) b) Enter the matrix A. gt;gt; A=pascal(5) To add a column of all ones to the right end of the matrix, execute the following command. gt;gt; A(:,6)=ones(5,1) 9. Enter matrices A and B. gt;gt; A=[2 3 1;0 1 2;0 0 5]; gt;gt; B=[1 1 4;0 0 5;3 5 2]; Calculate AB. gt;gt; A*B ans = 5 6 15 7 10 25 25 9 10 15. a) Enter the matrix A. 11. Enter matrix A. gt;gt; A=pascal(8); The following command will zero out all the odd columns. gt;gt; A(:,1:2:end)=0; gt;gt; A=ones(5); We’ll build a new matrix using the ? rst two roes of matrix A, then a row of 5’s, then the last three rows of matrix A. Note that we separate new columns with commas. 102 Chapter 2 Vectors and Matrices in Matlab gt;gt; B=[A(1:2,:);5*ones(1,5); A(3:5,:)] B = 1 1 1 1 1 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 b) Enter the matrix A. gt;gt; A=ones(5); We’ll build a new matrix using the ? rst 3 columns of matrix A, then a column of 5’s, then the last two columns of matrix A. Note that we separate new rows with semicolons. gt;gt; B=[A(:,1:3),5*ones(5,1), A(:,4:5)] B = 1 1 1 5 1 1 1 1 1 5 1 1 1 1 1 5 1 1 1 1 1 5 1 1 1 1 1 5 1 1 gt;gt; A=[1 2 3;4 5 6;7 8 9] A = 1 2 3 4 5 6 7 8 9 The next command will subtract 4 times row 1 from row 2. gt;gt; A(2,:)=A(2,:)-4*A(1,:) A = 1 2 3 0 -3 -6 7 8 9 b) Continuing with the last value of matrix A, the next command will subtract 7 times row 1 from row 3. gt;gt; A(3,:)=A(3,:)-7*A(1,:) A = 1 2 3 0 -3 -6 0 -6 -12 9. a) Enter the matrices A and B and compute C. gt;gt; A=magic(3); B=pascal(3); gt;gt; C=A+i*B The transpose of ? ? 8+i 1+i 6+i C = ? 3 + 1 5 + 2i 7 + 3i ? 4 + i 9 + 3i 2 + 6i 17. a) Enter the matrix A. Section 2. 2 is 8+i 3+i 4+i ? 1 + i 5 + 2i 9 + 3i ? . C = 6 + i 7 + 3i 2 + 6i T Matrices in Matlab 103 ? ? second dimension with the following command . You’ll note that the sum of each row is 260. gt;gt; sum(A,2) ans = 260 260 260 260 260 260 260 260 This result is veri? ed with the following Matlab command. gt;gt; C. ’ b) The conjugate ? 8+i ? 3 + 1 C= 4+i is 8? i 3? i 4? i ? 1 ? i 5 ? 2i 9 ? 3i ? . C = 6 ? 7 ? 3i 2 ? 6i T transpose of ? 1+i 6+i 5 + 2i 7 + 3i ? 9 + 3i 2 + 6i ? ? 23. Store A with the following command. gt;gt; A=pascal(5) A = 1 1 1 1 2 3 1 3 6 1 4 10 1 5 15 This result is veri? ed with the following Matlab command. gt;gt; C’ 1 4 10 20 35 1 5 15 35 70 21. Enter matrix A. gt;gt; A=magic(8) You sum the rows along the ? rst dimension with the following command. You’ll note that the sum of each column is 260. gt;gt; sum(A,1) You sum the columns along the You store I with the following command. gt;gt; I=eye(5) I = 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 Note that AI is identical to matrix A. 04 Chapter 2 Vectors and Matrices in Matlab You should be able to compute vwT manually and g et the same result. gt;gt; A*I ans = 1 1 1 1 1 1 2 3 4 5 1 3 6 10 15 1 4 10 20 35 1 5 15 35 70 27. Load the matrices A and B. gt;gt; A=ones(2); B=2*ones(3); Load the matrix C. gt;gt; C=3*ones(2);You can construct the required matrix with the following command. gt;gt; D=[A,zeros(2,3),zeros(2,2); zeros(3,2), B, zeros(3,2); zeros(2,2), zeros(2,3), C] A 256? 256 identity matrix would have 1’s on its main diagonal and zeros in all other entries. 25. a) Store the vectors v and w. gt;gt; v=(1:5). ’; w=(2:6). ; The inner product vT w is computed as follows. gt;gt; v. ’*w ans = 70 You should be able to compute vT w manually and get the same result. b) The outer product vwT is computed as follows. gt;gt; v*w. ’ ans = 2 3 4 6 6 9 8 12 10 15 29. The entry in row 1 column 1 would be H(1, 1) = 1/(1 + 1 ? 1) = 1. The entry in row 1 column 2 would be H(1, 2) = 1/(1+2? 1) = 1/2. Continuing in this manner, we arrive at a 4 ? 4 Hilbert matrix. ? ? 1 1/2 1/3 1/4 ? 1/2 1/3 1/ 4 1/5 ? H=? ? 1/3 1/4 1/5 1/6 1/4 1/5 1/6 1/7 This result can be veri? ed by these commands. 4 8 12 16 20 5 10 15 20 25 6 12 18 24 30 gt;gt; format rat gt;gt; H=hilb(4)

Twelfth Night Analysis Essay Example For Students

Twelfth Night Analysis Essay William Shakespeares Twelfth Night is set in a province called Illyria on the coast of Italy. The play is about a brother and sister, Sebastian and Viola, who are separated after a shipwreck, and both think the other has drowned. The play tells the tale of how they were eventually reunited. There are a wide range of characters in the play; ranging from Malvolio, Olivias steward, who is very self-centred with no sense of humour to Sir Toby who is always out enjoying himself and really just lives a life of pleasure. A caring character is Viola; she is not ne to upset other people. Olivia receives a lot of sympathy because she is mourning for her brother. Orsino has a comfortable but useless existence. He is rich but sits moping about love all day. All of these characters are different and each have their faults such as Sir Toby may be criticised for taking a lot of Sir Andrews money whereas Violas fault is that she is too nice, never wanting to cause anyone any harm. This is a fault be cause it may hold her back from doing a something that she should. We will write a custom essay on Twelfth Night Analysis specifically for you for only $16.38 $13.9/page Order now I think that Shakespeare has given the characters faults to ake them more interesting and realistic. Malvolio tries to impress Olivia but it does not work. Although she respects him she does not favour him, as he thinks, for having a good job. He is good at his job but should enjoy himself instead of thinking himself all the time. This is one thing that makes him an unlikeable character also he considers himself to be superior to other characters but no one really likes him and he does not know what they really think of him. Although he mostly cares about himself some of his love goes to Olivia. I think that he wants to be romantic but has a hard time expressing his feelings or does not want people to know what hes really like. His character does not really develop throughout the play, and I disliked him as much at the end as I did at the start of the play. Sir Toby is a likeable character because he does not care what anyone thinks of him, if they do not like him, they will just have to put up with it. People think he should be a respectable gentleman and act his age but he finds acting like everyone else stuffy and claustrophobic. Sir Toby is certainly not a model gentleman but when he drinks his behaviour is even worse. He does not have a lot of money. He may have had more but living a life of pleasure has changed that. He is criticised for living a life of pleasure but at least, unlike some other characters, he is genuine, he does not try to be anything he is not, and this is one of the reasons why Maria loves him. Although Sir Toby is a likeable Character his practical jokes do tend to get tiresome as the play wears on. Olivia, Sir Tobys niece, is not ike him at all. She is a well off countess who is respectable and acts the way she should. Olivia receives a lot of sympathy because she has lost her father and her brother, but Sir Toby does not think that her grieving is genuine. Olivia is quite a likeable character but I think that she is taking it a bit too far, saying she will never love another man again. It is likely that she enjoys all of the attention and sympathy that she is getting. Viola, the sister of Sebastian, has a lot going for her; she is intelligent, tactful, honest nd well educated and able to deal with people better than the other characters. She is a caring character who likes to get things done, she isnt one to just sit back and do nothing or let others do things for her. Being caring is one of Violas main features. She does not like to upset or hurt people and she would not mock people or make fun of them behind their backs. She carried out her commands and even though she was put in an awkward position she did not refuse for fear of upsetting someone. Some of Violas lines are he most poetic of the entire play and therefore, perhaps, are the ones which will be remembered the most. Duke Orsino does not seem to have much character or personality. .u4bea9f9b2829dc9e8b39faae14048a5b , .u4bea9f9b2829dc9e8b39faae14048a5b .postImageUrl , .u4bea9f9b2829dc9e8b39faae14048a5b .centered-text-area { min-height: 80px; position: relative; } .u4bea9f9b2829dc9e8b39faae14048a5b , .u4bea9f9b2829dc9e8b39faae14048a5b:hover , .u4bea9f9b2829dc9e8b39faae14048a5b:visited , .u4bea9f9b2829dc9e8b39faae14048a5b:active { border:0!important; } .u4bea9f9b2829dc9e8b39faae14048a5b .clearfix:after { content: ""; display: table; clear: both; } .u4bea9f9b2829dc9e8b39faae14048a5b { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u4bea9f9b2829dc9e8b39faae14048a5b:active , .u4bea9f9b2829dc9e8b39faae14048a5b:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u4bea9f9b2829dc9e8b39faae14048a5b .centered-text-area { width: 100%; position: relative ; } .u4bea9f9b2829dc9e8b39faae14048a5b .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u4bea9f9b2829dc9e8b39faae14048a5b .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u4bea9f9b2829dc9e8b39faae14048a5b .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u4bea9f9b2829dc9e8b39faae14048a5b:hover .ctaButton { background-color: #34495E!important; } .u4bea9f9b2829dc9e8b39faae14048a5b .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u4bea9f9b2829dc9e8b39faae14048a5b .u4bea9f9b2829dc9e8b39faae14048a5b-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u4bea9f9b2829dc9e8b39faae14048a5b:after { content: ""; display: block; clear: both; } READ: A Comparison Contrast of A Brave New World and 1984 EssayHe seems not to do very much, he has an almost useless existence; he just sits about moping about love. He is rich and has a comfortable existence with lots of servants. He seems young and immature, and does not have the same wisdom or knowledge as Viola and Sir Toby do. He is not an imposing figure, but it is possible that there is more to him than meets the eye. Orsino has ried with Maria but has not succeeded because she is in love with Sir Toby. It is too hard to form an opinion of him because he isnt a very noticeable character. I think that Viola emerges with credit at the end of the play because her only fault is that she is too nice so she could not be criticised for anything. Two characters who I think come out of the play badly are Sir Toby and Malvolio. Both of these characters can be annoying at times, and although Toby may have started off well he does end up quite boring, whereas Malvolio, on the other hand, was never a likeable character. Twelfth Night Analysis Essay Example For Students Twelfth Night Analysis Essay of Othello as a tragic hero and his correspondence to the canons for tragic protagonists. Othello and Aristotles Definition of Tragedy To decide how well Othello fits into the mold of a tragic hero, one needs to accept in the first place a working definition of tragedy and tragic hero. The theorists exploring tragedy almost universally draw upon the classic account of this play variety in Aristotles Poetics. The prominent Greek philosopher defined a heroic tragedy in the following way: A truly tragic plot is a disastrous reversal of fortune, coming, through his own fault, to a man of essentially noble quality, accompanied by the discovery that some other person or persons are not what they had seemedà ¢Ã¢â€š ¬Ã‚ ¦ test of a great tragedy is its power to cleanse the beholders emotions through the pity and fear which it awakens in them Othello: the tragic hero. This cleansing that is realised through pity and fear was termed catharsis and is an indispensable feature of any tragedy. We will write a custom essay on Twelfth Night Analysis specifically for you for only $16.38 $13.9/page Order now Besides, a tragedy needs a character of noble quality, guilty of some kind of fault that brings about tragic events. A tragedy also has to present to the reader a plot possessing some logical unity and completion and the one that contains engaging action. Aristotle also specified that a tragedy has to include appropriate linguistic devices that serve to bring out its meaning Time and the tragic hero. Most critics stopped short of saying that Shakespeare was aware of Aristotelian theories and took them as a guide for writing Time and the tragic hero; Djordjevic 2003. However, his tragedies reveal strict adherence to Aristotles theory, and Othello is no exception. Whether this correspondence was caused by a thorough study of Aristotles works or through an accidental coincidence of thoughts of two geniuses of the worlds culture remains a matter for guessing. Thus, the play definitely possesses a noble character, Othello. The mans nobility of action contrasts with his dark-colored appearance, unusual for Europe of that time. Othello proved himself to be a noble warrior deserving of the highest respect. He never acts dishonestly or cowardly throughout the play; in fact, nobility is one of the most important features of his character. Yet he fails through his own fault, and this fault is his credibility. An essentially good feature, it is taken to extremes in Othello, which causes his demise. He never stoops to questioning Desdemona. He is so absorbed in what Iago tells him that he never questions the words of the villain. At the time when the vicious Iago weaves his web of conspiracy, gullible Othello greets him with the words: I know thou art full of love and honesty. Therefore, Othello is not with bitterness, confessing that his ruin was brought about by his own failure: O cursed, cursed slave! Whip me, ye devils, from the possession of the heavenly sight! Blow me about the winds! roast me in sulphur! O Desdemona, Desdemona Dead! O! O! O! Othello as a play also fits Aristotle description as it contains logical unity and coherence that is a necessary component of tragedy. The play starts from the moment of idyllic honeymooning between Othello and Desdemona and follows Iagos treacherous plan from inception to its tragic success. Othellos sufferings in youth and the story of his courtship stay behind the scene, but in Othellos account they form an logical background for the action observed by the viewer. Othello evokes in the readers both pity and fear. They are pressured to feel sorry for the man who so sadly loses his wife due to a conspiracy. The pity for Othello even exceeds the feeling for Desdemona who is merely a victim; she does not have to suffer the pangs of conscience for what she has done. At the same time pity is not the only feeling Othello evokes in the readers or viewers. He also raises fear as a man capable of such a savage revenge, killing a wife on the spot for the alleged adultery. It seems that even at the time of more stringent morality such as mediaeval Italy not every husband would go that far as to kill the adulteress. This is even less likely in Elizabethan England, and so had to seem even wilder to Shakespeares contemporaries. Othellos reaction demonstrates that he was a man of extremely hot temper and strong emotions, capable of venting his sentiments in a very violent way. Othello: A Stock Comic Character? .u1e32c7f3a178f5673b35f05a7039e9bd , .u1e32c7f3a178f5673b35f05a7039e9bd .postImageUrl , .u1e32c7f3a178f5673b35f05a7039e9bd .centered-text-area { min-height: 80px; position: relative; } .u1e32c7f3a178f5673b35f05a7039e9bd , .u1e32c7f3a178f5673b35f05a7039e9bd:hover , .u1e32c7f3a178f5673b35f05a7039e9bd:visited , .u1e32c7f3a178f5673b35f05a7039e9bd:active { border:0!important; } .u1e32c7f3a178f5673b35f05a7039e9bd .clearfix:after { content: ""; display: table; clear: both; } .u1e32c7f3a178f5673b35f05a7039e9bd { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u1e32c7f3a178f5673b35f05a7039e9bd:active , .u1e32c7f3a178f5673b35f05a7039e9bd:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u1e32c7f3a178f5673b35f05a7039e9bd .centered-text-area { width: 100%; position: relative ; } .u1e32c7f3a178f5673b35f05a7039e9bd .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u1e32c7f3a178f5673b35f05a7039e9bd .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u1e32c7f3a178f5673b35f05a7039e9bd .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u1e32c7f3a178f5673b35f05a7039e9bd:hover .ctaButton { background-color: #34495E!important; } .u1e32c7f3a178f5673b35f05a7039e9bd .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u1e32c7f3a178f5673b35f05a7039e9bd .u1e32c7f3a178f5673b35f05a7039e9bd-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u1e32c7f3a178f5673b35f05a7039e9bd:after { content: ""; display: block; clear: both; } READ: The Night Of The Hunter: The Preacher EssayAlthough the standard view is to see Othello as a purely tragic character, other, mopre unusual interpretations are possible. Igor Djordjevic in his article Goodnight Desdemona Good Morning Juliet: From Shakespearean Tragedy to Postmodern Satyr Play points out an interesting aspect of Othellos character. In his view, Othello could have been a comic fellow instead, and he is inverted into a tragic hero by the playwright. Othello is a character typical of comedies; a husband whose wife is much younger and more beautiful, and thus raises fears of being deceived. However, Othello does not fit into the regular model of a husband whose worries are to be derided. At the outset of the play he appears as a lover who must obtain the legitimization of his courtship of Desdemona, and he must overcome the multiple obstacles of the senex, racial prejudice, and religious charges of witchcraft Djordjevic 2003. It is his painful pursuit of Desdemona whom he had to steal to be able to marry her that wins him the hearts of the reader. Shakespeare depicts the trials of Othello, a victim to racial bias, in such a way that the reader begins to sympathise with the late love of this great man, the swan song of his life that is already to some degree tragic. Seeing him lose what he worked so hard to attain endears him to the reader even more. Othello evokes pity in the reader partly due to the fact that he experienced so many hardships in life that the skilful narrative of these hardships eventually won him Desdemonas heart: She loved me for the dangers I had passed, And I loved her that she did pity them. The playwright tries here to instil in the reader sympathy with the old soldier who fought desperately for his love going through many hardships. The listener responds by saying I think this tale would win my daughter too, and this approval symbolically à ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦ upon him the approval and affection of the fictional worlds power structures Djordjevic 2003. Is Othello Real? Now we will turn in our discussion to a possible objection to the fact that Othello is a tragic hero. Some criticism of his belonging to this category comes from the speculation concerning the realism and probability conveyed by Othello which suggests that because of the seeming unlikelihood of the events in the play, it is not characteristic of a tragedy Sharina. Indeed, the plot develops in a rather speedy manner and the playwright does not elaborate on Othellos or other characters. Even so, the action seems unrealistic only at first glance. First, it is a mode of the artist to show the public the unusual and the unexpected basing these things on the knowledge of everyday things that are familiar to everybody. Shakespeare here makes his audience see jealousy in a new light, and it is no wonder that the name of Othello has come to be a generic name for a jealous husband. It is positive that reading through the story had a deterrent effect on the behaviour of many violent husbands who could have stopped short of beating their wives to death in a family quarrel provoked by suspicions of infidelity. And is such a scenario an unlikely one? Women die in family battles even in most developed nations of the world today, and the examination of domestic violence statistics may show that wife murder is unfortunately still a prevalent phenomenon even after centuries of struggle for gender equality and reduction of crime rate. If we consider that things that are unusual in our own environment may unfortunately be prevalent in the lives of other social groups, we will see that events in Othello are not that unusual. The fact that Othello is easily persuaded to murder his wife by Iago should not be regarded as totally unrealistic either. This is what Aristotle would describe as hamartia à ¢Ã¢â€š ¬Ã¢â‚¬Å" the characters tragic flaw. For Othello, it is his naivetÃÆ' © and credulousness. His devotion comes to be exploited by one of the most ingenious villains in the history of literature. Iagos motives appear clear. Indeed, so many evil actions are committed every day due to jealousness that Iagos behaviour should not be surprising. In this character, viciousness is combined with deep psychological insight and potential for intrigue that are worthy of a better application. To count as Othellos close friend and ally, Iago had to be an outstanding player skilfully performing the part of the devoted ensign. He manipulates Othello to bring about his ruin in a way in which Othello would never be able to manipulate him. The events in the play may lead the reader to question why Othello is so ready to trust Iago and unwilling to trust his beloved wife Desdemona, a fact that generates the protagonists tragic flaw. .u9596c343747ab067670ec7e2795c610c , .u9596c343747ab067670ec7e2795c610c .postImageUrl , .u9596c343747ab067670ec7e2795c610c .centered-text-area { min-height: 80px; position: relative; } .u9596c343747ab067670ec7e2795c610c , .u9596c343747ab067670ec7e2795c610c:hover , .u9596c343747ab067670ec7e2795c610c:visited , .u9596c343747ab067670ec7e2795c610c:active { border:0!important; } .u9596c343747ab067670ec7e2795c610c .clearfix:after { content: ""; display: table; clear: both; } .u9596c343747ab067670ec7e2795c610c { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u9596c343747ab067670ec7e2795c610c:active , .u9596c343747ab067670ec7e2795c610c:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u9596c343747ab067670ec7e2795c610c .centered-text-area { width: 100%; position: relative ; } .u9596c343747ab067670ec7e2795c610c .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u9596c343747ab067670ec7e2795c610c .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u9596c343747ab067670ec7e2795c610c .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u9596c343747ab067670ec7e2795c610c:hover .ctaButton { background-color: #34495E!important; } .u9596c343747ab067670ec7e2795c610c .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u9596c343747ab067670ec7e2795c610c .u9596c343747ab067670ec7e2795c610c-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u9596c343747ab067670ec7e2795c610c:after { content: ""; display: block; clear: both; } READ: How To Cite A Short Story In An EssayThere several possible explanations for this apparently surprising behavior. First, Othello has come to rely on Iago in numerous mutual adventures where both risked their lives. The time itself spent together justifies the trust Othello puts in Iago. Perhaps to that point he had never come across the betrayal of a close male friend, except for Cassio, but there the conflict, in Iagos suggestion, was caused by the woman. Second, Othellos relationship with Desdemona arrived at the time when he probably had lost hope for a happy family life. She appeared as a star on the horizon to illuminate his life, and all the time he probably doubted that he could be a proper match for the beautiful girl she was. The idea that she is betraying him with someone else, someone younger, more handsome and closer to her in terms of background, social rank and status, falls on ready ears. This is something Othello had feared to hear for a long time, in spite of the seemingly idyllic love between him and his wife. Thus, Othellos actions seem closer and more understandable to us than seems at first glance. And it is action, not characterization that makes a tragedy, according to Aristotle Sharina. That is why he is a real tragic character. Comparison to Other Tragic Heroes Othello is similar to and different from other characters in other plays by Shakespeare. Of all the characters, he probably falls most of all due to his own tragic fault, and Aristotles hamartia is most evident in this case. Other characters such as King Lear, Hamlet, Macbeth, Romeo, have to fight evil in a more open form. Hamlet, for instance, has to deal with the betrayal of his father-in-law and mother. True, he has to obtain proof of their betrayal, which is the reason he suspends the revenge desired by his father. But there is hardly a reason to blame Hamlet from the point of view of modern liberal criminal justice that places emphasis on preserving the rights of the suspected. Hamlet acts on the evidence he has, and his indecisiveness is the direct consequence of his responsible attitude towards revenge. King Lear, in his turn, falls victim to his paternal feelings. His misfortune was brought about by his extreme trust in his daughters, but few readers would expect a father to act in distrust of ones children. Mothers and fathers forsaking all they have for their children are praised and respected in our society that highly appreciates such behavior. The fact that daughters turned out to lack gratitude is an example of undisguised evil that can, as many people think, happen to the best of parents. These two characters are definitely not villains; rather, they fall prey to evil people eager to take advantage of some traits of their characters that under other circumstances are most worthy. Strictly speaking, their actions cannot even be named mistakes from the moral, not strategic, point of view. Macbeth, on the other hand, is a straightforward villain, and his ruin is the result of his own treacherous acts. He yields to ambition, killing Duncan, to become King of Scotland. A virtuous reader has little ground to associate oneself with this character and simply observes a tale of how a villain is brought to ruin through his deeds. Othello, on the other hand, is essentially a moral person who fails through making a terrible mistake. Conclusion Thus, Othello is a bona fide tragic hero, even if he is not a man of unusual stature or appearance. He possesses all the vital traits of the tragic character, noble qualities, pure character, and a tragic fault, his naivetÃÆ' © that makes him vulnerable to the intrigues of his antagonist, Iago. A staple comic character, a deceived husband, he is turned into a really tragic personage by the sympathy with which Shakespeare describes his misfortune. His tribulations, although somewhat unrealistic at first glance, are in line with the everyday happenings even in contemporary world. Othello stands out from other tragic heroes, because he falls through his own flaw and yet his flaw is so minor that is incomparable with the misfortunes he suffers.

Costly Business Case Utilities Co.

Costly Business Case Utilities Co. Introduction Utilities Co. was keen on cutting 120 jobs because of the tough economic climate and escalating competition. Maree Davis, the HR Manager of the company was at the centre point of implementing the plan of cutting the workforce.Advertising We will write a custom case study sample on Costly Business Case: Utilities Co. specifically for you for only $16.05 $11/page Learn More The CEO indicated that the redundancies were voluntary, but it emerged later that the plan targeted specific workers in the middle level management. The strategy of downsizing the workforce had two stages. The first stage was to make a public statement on the intention to dismiss employees and the second stage was to use targeted redundancies. However, the announcement invited attention from the press and state politicians because of industrial action to protect jobs. Similarly, the announcement led to severe work-related stress as many employees were in fear of losing their jo bs. In particular, the company received negative messages from the press and customers who were dissatisfied with service delivery at the time. As HR manager, Maree found it difficult to implement the strategy because she felt that the CEO’s decision was challenging and it was virtually impossible to identify 120 redundant jobs. Although she received voluntary redundancies from 52 employees, there was a lot of dissatisfaction. On the other hand, the CEO was relentless on implementing the layoff plan despite efforts for negations from the union and advice from HR department. Surprisingly, the targeted redundancies did not express interest in voluntary redundancy, thus triggering the need to enter the second phase of the plan.Advertising Looking for case study on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More At this point, Maree resigned from his position because she felt that the decision to lay off many older employees could lead to troubles with Human Rights Commission. Therefore, this paper analyses the case of Utilities Co. with reference to HR implications of the CEO’s announcement to lay off 120 staff. The paper also explains the OHS concerns that arose in response to the announcement, and outlines recommendations to improve OHS during layoffs. Similarly, the third section of this paper evaluates the impact of industrial action on the organisation. Finally, the recommendation section discuses an ideal organisation’s plan to communicate the layoff decision to employees and managers. HR Implications of CEO’s Announcement to Lay off Staff The CEO’s announcement emerged because of the claims that the Utilities Co. was experiencing tough economic times and increasing competition. As a result, the company wanted to get rid of underperforming staff to remain competitive in its market segment. The CEO was in an unfortunate position of determining the bette r alternative of dismissing workers. The announcement was an indication that the company was determined to downsize its workforce, but the figure was quite alarming and consequently led to shock and disorder within the company. The workers, including the HR manager, were unhappy about the announcement because it would cost them their positions in the company. In addition, the announcement implied that the company’s management was poor because it elicited some interesting facts about employment relationship within the company. First, Maree had identified that the company had few workers in some significant areas.Advertising We will write a custom case study sample on Costly Business Case: Utilities Co. specifically for you for only $16.05 $11/page Learn More This meant that it was difficult to identify 120 redundant jobs despite the CEO’s suggestion that the exercise targeted underperforming middle managers. Second, the company did not relate w ell with its employees because expert staff expressed interest in voluntary redundancies, but the target group did not express interest in the process. This meant that the company was to lose its productive workforce. It is surprising how the company lacks proper procedures of communicating lay offs to its employees. In the light of the HR conflicts brought about by CEO’s announcements, it is essential to understand employment relationship in managing workplace relations. The perspectives of employment relationship help us to understand how an employee and an employer relate. Employment relationship entails managing staff for successful objectives of the organisation while taking into consideration worker’s anticipations (Chambliss, 2007). However, Utilities Co. did not consider the expectations of employees with regards to work ethics, moral, team contribution skills, motivation, and general aptitude. Furthermore, findings from studies indicate that employment relatio n is mainly open-ended, spontaneous, and an inclusion of contradictory theories about conflict, control, and regulation. The perspectives of employment relations are: utilitarianism, pluralism, and Marxism (Bateman Snell, 2009).Advertising Looking for case study on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More However, the pluralist view of employment relationship is a good example of explaining the situation at the company. Pluralists perceive an organisation comprising of powerful and different sub-groups, including management and trade unions. This viewpoint considers conflicts as a common aspect in organisation because the employer and employees have dissimilar interests; the CEO’s objective is to reduce the number of employees in order to cut down the company’s expenses while employees’ interest is retaining their occupations and enhancing their welfare. Kramar et al. (2011) argue that different organisations with disparate management also engage in establishing guidelines of employment. Detection and control of conflicts is imperative in determining the best approaches of problem solving. Additionally, the management’s role is to coordinate and persuade employees to harmonize the different interests rather than enforcing rules that would compromise negoti ations. Trade unions are recognized as genuine agents of employees, thus such organizations advocate for collecting bargaining which helps in dealing with conflicts. Thus, employers should accept and expect to resolve conflicts through legitimate measures of dealing with disagreements (Brewster, 2008). According to Roethlisberger (2009), pluralism derives its ideas from the point of view of Donovan Commission, which started in 1965 to assess the rising conflicts in industrial relations practices. Pluralism was important in its analysis on management: unlike the unitary approach where there are no authentic grounds for conflicts, managers in a pluralistic system should accept conflicts and seek feasible procedures of avoiding them. Thus, the first basis of pluralism is that the organisation should have industrial relations and personnel professionals who provide staffing and collective bargaining counsel to managers (Brewster, 2007). Second, external arbitrators are required to help in conflict resolution. Third, the management should recognize trade unions when analysing employee sentiments. Finally, the management should establish a good environment for collecting bargaining with union representatives. Therefore, it is apparent that successful industrial relations involvements such as collective bargaining can resolve disputes. Unlike the unitary system, the pluralist theory provides alternative solutions to conflicts, thus the management must exercise control and regulation, considering the requirements of trade unions and the state. Similarly, pluralist engage all participants in conflict resolution, thus favourable solutions are open to discussion. This follows the notion that conflicts are important in understanding the major tensions in an organisation and therefore the management should not ignore them. Furthermore, the theory advocates for divergent employee relations rules. Some organizations can decide to deal with employee organizations instead of t rade unions, while other organizations can work with trade unions to enhance employee commitment. In essence, pluralism is appropriate for a collective industrial relations system because trade unions are involved in conflict resolution (Bateman Snell, 2009). However, the major disadvantage of pluralist perspective, which the case depicts, is emphasis on rules and procedures, but it ignores other factors that affect or contribute to resolving disputes. For example, through industrial relations, organisations can formulate rules that determine the steps of resolving conflicts. However, such rules may not apply to different working environment. Likewise, the theory fails to note that the state not only considers the interests of the public, but also business interests. Dekler (2007) argue that focusing on employee interest may hinder the process of collective bargaining. Likewise, the redundancies raised equity issues within the company. The concept of equity relates to satisfaction in relation to expectations of fair and/or unfair allocation of resources in the HR perspective (Kramar, 2011). The equity issues depicted in the company are flexible work and discrimination. The communication strategy assumed by the CEO and organisational factors affected the flexibility of work. According to Boxall Baron (2004), essential communication, from Human Resource perspective, stresses the open relations between the organisation and employees. This results to goals being realized, which in turn improve the company’s performance. However, Utilities Co. did not express the need to enhance effective communication. The management communicated the lay off news without considering workers’ reactions. As a result, employees exhibited low productivity since the customers were complaining. Several factors affect work behaviour. First, people within the company have different positions, relations, and views. The relationship between individuals of various departments with regards to management level determines how they behave. Workers tend to conform to their line manager more often as compared to managers of other departments (Godard, 2010). Customers also influence the way employees perform their duties, as there exist the need to satisfy customers. In addition, organisational goals shape the way employees work. The goals of an organisation are the reason for existence. Managers direct the activities of the organisation to the attainment of goals. The goals of an organisation will determine the nature of its inputs and outputs, the series of activities to acquire the inputs, and interactions with its external environment (Decenzo Silhanek, 2002). Furthermore, culture reflects the underlying assumptions about the way of performing work; what is acceptable and not acceptable, and what actions and behaviour are encouraged and discouraged within a company. Organisational structure underlines the manner of arranging individuals and groups with re spect to the task they perform. The culture and structure of an organisation develop over time and in response to a complex set of factors affecting work behaviour. The key factors that affect the development of any corporate culture include history, primary function and technology, goals and objectives, size, location, management and staffing, and the environment (Schmidt, 2009). On the other hand, discrimination was evident through the redundancies. As outlined by Maree, the CEO targeted older employees who held managerial positions and were receiving higher wages. Such employees were mainly 50 or older, and a move to lay them off would imply that the company discriminates people according to age. Similarly, the CEO’s argument that the targeted groups were underperforming was inconsequential because the team manages and controls the organisation; laying them off would worsen the current situation. OHS Concerns in Response to the Announcement The announcement to downsize the workforce had adverse effects on staff safety, health, and welfare. Lay offs often entail major changes to work processes because there is redistribution of tasks to a smaller number of staff, alterations to job descriptions, and changes to training (White-Means Hersch, 2005; Quill, 2005). The first reaction to the announcement was shock, which led to fear and decreased productivity. In addition, the OHS team received stress-related claims from workers who expressed their stress through anxiety disorders and depression. For instance, an employee became physically violent towards colleagues. In particular, Maree experienced stress-related sickness in the process of making difficult decisions within a short time. She was in a dilemma while trying to identify 120 redundant jobs and improving understaffed areas. For example, industrial action compromised the process because the HR staff received numerous abusive messages from both the press and customers; Maree ignored the messages, b ut felt sick. Besides, the CEO gave a short notice to persuade Maree to execute the layoff plans. According to Quinlan (2007), job insecurity and bad working relations (as the ones depicted in the case) correlate with undesirable effects on worker safety and health because there are fears that arise from new informal means of communication between employees. However, the OHS team in the company was overwhelmed with complaints from distressed staff members. Similarly, some unsatisfied staff accepted the call for voluntary redundancies, which led to cutbacks in customer service areas. This indicates that the organisation was not keen on supporting staff affected by the announcement; it is surprising that the CEO was happy with the process, and he did not consider worker’s wellbeing. For instance, Maree had to support her own staff and other organisational activities because many workers were unable or reluctant to adjust to the changes in workplace conditions. In light of OHS c oncerns in the organisation, the OHS team should embark on a risk assessment of the OHS effects of the layoffs, discuss with employees and their representatives, and manage the risks without interfering with current OHS standards (Dragano, Verde, Siegrist, 2005). This is in a bid to improve OHS during layoffs. The risks stem from personal factors that affect work behaviour. The HR department should assess the factors that affect work behaviour during layoffs. Work behaviour analysis encompasses the methodical assessment of the nature and components of a well-defined job (Armstrong Baron, 2004). The OHS team should identify individual differences such as gender, marital status, and tenure because they affect work behaviour. The obvious differences between men and women affect job performance. There exist no systematic male and female differences in analytical abilities, competitive focus, problem-solving skills, and decision-making skills. Researchers believe that women are more wi lling to abide by the rule of work and men are insistent and more likely to have expectations of achievement (Johnstone, Quinlan, Walters, 2005). Another issue that seems to differ between male and female employees is the preference for job environment; women mainly prefer an organisation that caters for their wellbeing (Mullins, 2004). For instance, Maree found that some women accepted voluntary redundancies because the organisation does not respect people. Work experience through tenure also affects work behaviour. Moreover, if person stays long in a job, chances are few that he or she will quit. Thus, tenure and satisfaction are concurrently related (Moore, Grunberg, Geenberg, 2004). This explains why the old employees of Utilities Co. were reluctant in taking voluntary redundancies. In essence, the equity officer analysed the demographic profile of workers who had quit their jobs on voluntary redundancies and found that many younger staff and women had taken redundancies. Seco nd, personality tends to predict behaviour and happiness related to work. These behaviours include absenteeism, performance, and team effectiveness. Personality matters when we combine different personality, thus achieving a stronger relationship between work performance and personality. Third, what people perceive determine how they perform their work-related activities. For instance, the layoff announcement shocked workers because they knew that their jobs were insecure, and therefore they felt disappointed by the organisation. Fourth, values help individuals to determine what is good, right, or desirable. Values help in the analysis of organisational behaviour and hence managers can be able to accommodate individuals from different cultures. Since values differ across cultures, understanding such differences is helpful in predicting employee behaviour from various cultures. Finally, attitudes affect work behaviour because they reflect how employees feel about the work. Attitude i nvolves the aspects of cognition, affect and behaviour. Cognitive facet of an attitude is a belief in something; for instance, grapevine is wrong. Affective facet of attitude is the emotional or feeling part of attitude, while behavioural facet of an attitude is an intention to act in a particular way towards somebody or something (Sverke, Hellgren, Naswall, 2002). Another recommendation for Utilities Co. is to provide help documents on layoffs to explain the role of OHS team and staff in order to improve OHS. The documents should take into consideration the factors explained in the previous paragraphs because they are the ones that lead to health issues during downsizing. The Impact of Industrial Action on the Organisation The workers union responded to the layoff announcement by engaging in industrial action in order to prevent massive layoffs. The union felt that the redundancy process was unfair. As one of the steps towards industrial action, the union applied for protected ind ustrial action through the Fair Work Australia (FWA). Besides, the union though that the pending enterprise bargaining agreement (EBA) was one of the major contributing factors of the redundancies. In light of the union campaign, there was keen interest from the media and national politicians because Utilities Co. was a big and formerly state owned business. This made the CEO to engage the company’s lawyers in devising plans to proceed with layoffs. The CEO defended his decisions by citing that the company wanted to stay afloat in the current economic problems. Besides, he agreed to proceed with negotiations on a new EBA because of pressure from the union. However, the ongoing industrial action surpassed the hostile meetings as it became gradually more disruptive and reduced the quality of service delivery. The company received many customer complaints and it was difficult to reach out to new customers because constant negative press was taking effect. Many HR workers receive d abusive e-mails and experiences emotional stress. However, the union did not achieve its major objective because the company proceeded to subsequent processes of cutting down its workforce. The industrial action only tainted the company’s image and facilitated the layoff process. Interestingly, the company postponed the EBA negotiations because of industrial action. In fact, the EBA meetings were not successful because the union opted for industrial action before considering the option of negotiations. The fallout of EBA negotiations meant that the company was determined to lay off employees. Although the CEO indicated that the redundancies were voluntary, the second phase of downsizing was compulsory redundancies, which targeted one third of middle management positions. The union could have opted for negotiation with the company through collective bargaining. Since there was an existing EBA, it was necessary to cite the guidelines in the agreement to avoid conflicts. In th e negotiations, the union could have cited unfair dismissal laws to persuade the company to retain workers or offer notice and full redundancy benefits (Artz, 2010). Another argument that the union could have used in the negotiation is that the company breached the Australian labour laws because the redundancies were not genuine. According to Decenzo Silhanek (2002), redundancy arises where an employer does not require a worker’s job and someone else cannot take the work. However, from the case, Maree found out that some important areas within the Utilities Co. were having few staff and it was difficult to identify 120 redundant jobs. In fact, it would be appropriate to consider the company’s action as unfair termination. This could have been a good discussion point because unfair dismissal laws is important to make sure both that employees can confront unjust termination, and to act as a guideline for employees who would layoff workers unfairly. In essence, understan ding the unfair dismissal laws could have been a significant step in ensuring safety and fairness in Utilities Co. Recommendations Maree resigned from her HR position because she was unable to work under pressure. This is evident because abuses from customers made her sick. If I were in the same position, I would not have resigned because such challenges are common in the workplace and it was a matter of executing what the company had initiated, but the process was wrong. Maree should have conducted thorough investigation of the company and communicated her findings to the CEO. However, she did not provide feasible suggestions to the CEO. For instance, Maree noticed that the company had few workers in some critical areas, but she did not explain it to the CEO. The CEO needed assurance that the company can weather the tough economic climate and increasing communication without necessarily cutting down the workforce. Maree failed to identify other significant factors that contribute t o productivity. The best approaches of increasing workplace productivity are positive management and good communication. In the place of work, managers who exercise positive means and enhance positive behaviour can achieve positive results. The managers must have broad knowledge and act as the intellectuals of the organisation. When disagreements arise within the organisation, it is the manager who advices the administrators on the approach to employ towards solving the problem amicably. Other matters that require the counsel of HR manager include appraisal, training, recruitment and incorporations (Kramar et al., 2011). As a matter of consideration, the manager understands the capacity of the organisation much more than anybody else. For instance, the manager is responsible for designing the tasks for every employee and thus he/she has to be involved when the organisation intends to hire and/or layoff staff (Dekler, 2007). Moreover, with regards to the layoff decision by the CEO, t he ideal organisation plan to communicate the decision would include good communication strategies, honesty, respect towards employees, asking feedback, ensuring commitment to employees’ safety and wellbeing. First, the organisation should share all the information regarding layoffs, citing the major reasons and implications to workers. The management should not imagine that workers understand the message at once or communicate only when all details are available. Consistent and accurate information is better in order to avoid rumours. Second, clarity of the decision to layoff workers might help them prepare, thus avoiding distractions like stress (Maertz et al., 2010). If the company does not know the exact number of redundancies, it is important to suggest a reasonable number. The company should make promises that are conceivable through exercising credibility. Third, the organisation should have guidelines that allow room for respect and dignity towards employees. For inst ance, a manager can exercise respect through giving the dismissed worker a chance to say goodbyes or letting him time to thank and/or receive thanks from colleagues. Fourth, the organisation should ask for feedback from various sources. Listening to employee’s suggestions or questions enhances organisational support to workers. The HR managers can administer questions, such as: How can we communicate better the layoff decision? Are there any major issues regarding how the layoffs are conducted? (Hershey, Blanchard, Johnson, 2008). Finally, it is important to restate the organisation’s commitment to health and welfare where possible. The organisation should focus on safety by expressing the likely effects of layoffs and the necessary reactions expected from employees to reduce the effects. For instance, a supervisor can take some time to ask each affected employee in his line of work how they are fairing with the changes. In this case, the supervisor can deal with the employees’ problems while focusing on work and enhancing safety measures. Conclusion The CEO and HR manager of Utilities Co. were in an unfortunate position of finding an appropriate strategy to lay off workers. Administering layoffs is often difficult because it involves dealing with people and factors that affect work behaviour. This paper analysed the implications of announcing layoffs, the concerns of OHS, the impact of industrial action on the organisation, and proposed an ideal organisation’s plan to communicate the layoff decision to the staff. The major HR implication of CEO’s announcement to lay off staff was that the HR department would work hard to identify redundancies within the company and consequently restructure the working environment. The announcement was received with shock from employees, and it led to decreased morale and productivity. As the HR manager, Maree was required to support her own staff and troubleshoot across the organisation in order to maintain the company’s operations. In addition, the announcement increased the OHS concerns as the news stressed many employees, and they even felt sick. As a response to the announcement, the union’s industrial action interfered with service delivery, but did not stop the company’s stand on dismissing workers. Therefore, the major recommendation for Utilities Co. is to have a feasible plan to communicate the layoff decision to the staff through the following five strategies: good communication strategies, honesty, respect towards employees, asking feedback, ensuring commitment to employees’ safety and wellbeing. 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