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Applications of Matrices to Business and EconomicsScribd Upload a Document Search Books, Presentations, Business, Academics... Explore Documents Books - Fiction Books - Non-fiction Health & Medicine Brochures/Catalogs Government Docs How-To Guides/Manuals Magazines/Newspapers Recipes/Menus School Work + all categories Featured Recent People Authors Students Researchers Publishers Government & Nonprofits Businesses Musicians Artists & Designers Teachers + all categories Most Followed Popular Ahmed Zubairu How does Scribd know my name? We are using Facebook to personalize your experience on Scribd. Learn More Account My Home View Public Profile My Documents My Collections Messages Settings Help Log Out Welcome to Scribd - Where the world comes to read, discover, and share... We’re using Facebook to give you reading recommendations based on what your friends are sharing and the things you like. We ve also made it easy to connect with your friends: you are now following your Facebook friends who are on Scribd, and they are following you! In the future you can access your account using your Facebook login and password.Learn moreNo thanksSome of your friends are already on Scribd:

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Exit Fullscreen Select View Mode View Mode Book Slideshow Scroll Readcast Add a Comment Embed & Share Reading should be social! Post a message on your social networks to let others know what you re reading. Select the sites below and start sharing. Link accountReadcast this DocumentReadcast Complete!Click send to Readcast!edit preferences Set your preferences for next time... Choose auto to readcast without being prompted. Ahmed ZubairuAhmed ZubairuLink accountAdvancedCancel Add a Comment View commentsShare & Embed Add to Collections Download this Document for FreeAuto-hide: on Ads by Google African Business Software Billing software for South-Africa Download now and have a try! africansoftware.co.za/billing Business Books Online shopping for millions of biz books at everyday low prices! www.debonairbookstore.com Industrial Microwave Industrial Microwave design, parts Industrial Microwave generators www.awimicrowaves.com/industrial/ Methodware World leading producer of risk management software www.cqs.co.za/methodware Paper XI Business Mathematics PROJECT ON Applications of Matrices to Business and Economics Made By: Akash Gupta - 1- Contents Topic Page No. •Acknowledgements •Introduction •Application of Matrix Addition and Subtraction •Application of Matrix Multiplication •Application of System of Linear Equations •Leontief’s Input-Output Model •Bibliography 2468 13 18 25 - 2Applications of Matrices to Business and Economics What is a Matrix? A matrix is a two-dimensional arrangement of numbers in rows and columns enclosed by a pair of square brackets ([]), in the form shown below. mn m m n n a a a a a a a a a 2 1 2 22 21 1 12 11 The above figure shows anm × n matrix ofm rows andn columns. Matrices are used to describe linear equations, keep track of the coefficients of linear transformations and to record data that depend on multiple parameters. They can be added, multiplied, and decomposed in various ways, which also makes them a key concept in the field of linear algebra. The subject of matrices has been researched and expanded by the works of many mathematicians, who have found numerous applications of matrices in various disciplines such as Economics, Engineering, Statistics and various other

sciences. In this project, the following applications to matrices will be discussed: •Applications of Matrix Addition and Subtraction •Applications of Multiplication of Matrices •Applications of System of Linear Equations •Leontief Input-Output Model - 3- But first, let’s discuss how various situations in business and economics can be represented using matrices. This can be done using the following examples. 1. Annual productions of two branches selling three types of items may be represented as follows: Branch Item A Item B Item C I II 2. Number of staff in the office can be represented as follows: Peon Clerk Typist Head Clerk Office Superintendent 3. The unit cost of transportation of an item from each of the three factories to each of the four warehouses can be represented as follows: Warehouse Factory W1 W2 W3 W4 I II III - 42969 3214 7542 2314 2876 2000 11342 11 18 15 16 19 11 26 22 14 17 12 13 Applications of Matrix Addition and Subtraction The applications of addition and subtraction of matrices can be illustrated through the following examples: Illustration 1 - The quarterly sales of Jute, Cotton and Yarn for the year 2002 and 2003 are given below. A= 15 15 20 15 10 18 20 10 20 22 25 20 B= 10 15 30 8 10 18 20 5 20 20 15 10 Find the total quarterly sales of Jute, Cotton and Yarn for the two years. Solution – The total sales of Jute, Cotton and Yarn will be obtained as under A+ B = 15 15 20 15 10 18 20 10 20 22 25 20 + 10 15 30 8 10 18 20 5 20 20 15 10 = 25 30 50 23 40 33 40 15 40 42 40 30 - 5- Jute Cotton Yarn Jute Cotton Yarn QI Q2 Q3 Q4 Year 2002 Year 2003 Illustration 2 – X Ltd has the following sales position of its products A and B at its two centers P and Q at the end of the year Y= 70 60 45 50 If the sales for the first three months is given as Q = 20 20 15 30 Find the sales position for the last nine months. Solution – Given are the sales positions for the whole year (Y) and for the first three months (Q). Hence, sales position for the remaining nine months – Y– Q = 70 60 45 50 20 20 15 30 = 50 40 30 20 - 6- AB P Q B AB P Q B AB P Q B Applications of Matrix Multiplication It is important to note that two matrices can be multiplied if and only if the number of columns of the first matrix equals the number of rows of the second. The resultant matrix will have the number of rows equal to the first matrix and number of columns equal to that of the second matrix. In other words, •A matrix of the order [ax b] can only be multiplied with a matrix of order [bx c] •The resultant matrix will be of the order [ax c] The application of multiplication of matrices can be illustrated through the following examples. Illustration 3 – Ram, Shyam and Mohan purchased biscuits of different brands P, Q and R. Ram purchased 10 packets of P, 7 packets of Q and 3 packets of R. Shyam purchased 4 packets of P, 8 packets of Q and 10 packets of R. Mohan purchased 4 packets of P, 7 packets of Q and 8 packets of R. If brand P costs Rs 4, Q costs Rs 5 and R costs Rs 6 each, then using matrix operation, find the amount of money spent by these persons individually. Solution – Let Q be the matrix denoting the quantity of each brand of biscuit bought by P, Q and R and let C be the matrix showing the cost of each brand of biscuit. Q = 3 3 8 7 4 10 8 4 3 7 10 × C= 1 3 654 × Since number of columns of first matrix should be equal to the number of rows of the second matrix for multiplication to be possible, the above matrices shall be multiplied in the following order. Q×C = 8 7 4 10 8 4 3 7 10 × 654 - 7- Ram

Shyam Mohan P QR PQR Ads by Google Applications of Matrices to Business and Economics Download this Document for FreePrintMobileCollectionsReport DocumentReport this document? Please tell us reason(s) for reporting this document Spam or junk Porn adult content Hateful or offensive If you are the copyright owner of this document and want to report it, please follow these directions to submit a copyright infringement notice. Cancel This is a private document. Info and Rating Reads:11,186 Uploaded:09/10/2009Category:Research>Business & EconomicsRated:Project on Applications of Matrix Theory to Business and Economics. Subject: Business Mathematics BusinessEconomicsmatrixApplicationsmatricesapplications of matrices to business and economics(more tags)BusinessEconomicsmatrixApplicationsmatricesapplications of matrices to business and economicsmatrix operationsexamples businessmatrix aplicationaplication economicsuse matrixmaticessolved examplesnotationsbuisnesssolved matrixb carrespectively(fewer)Followgupta_akash88 Ads by Google 100s of Cdn digital mags Get your favourite Canadian magazine in digital format! magazinescanada.zinio.com Business Form Software Fill-in the Blanks & Write Your Business Forms in a Snap ! Biztree.com SA Procurement Training World Class Procurement Training and claim the cost back in SA! www.commercedge.net Performance Management Create Organizational Alignment Manage Employee Excellence www.DSPanel.com Editors from Harvard Yale Admissions, Science, Business Gurus ONE or TWO Day Service www.gurufi.com Sign Up for an Ad-Free Scribd Remove all ads. Never see ads on Scribd again. No Thanks Share & Embed Related Documents PreviousNext35 p.35 p.30 p.17 p.40 p.21 p.33 p.13 p.34 p.188 p.31 p.6 p.23

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