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Paper XI Business Mathematics PROJECT ON Applications of Matrices to  Business and Economics - 1 -

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Made By:  Akash Gupta Contents Topic Page No . - 2 -
Acknowledgements Introduction Application of Matrix Addition and Subtraction Application of Matrix Multiplication Application of System of Linear Equations Leontief’s Input-Output Model Bibliography 2 4 6 8 13 18 25 Applications of Matrices to  Business and Economics - 3 -

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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 an m × n matrix of m rows and n 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 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: - 4 -
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 W 1 W 2 W 3 W 4 I II III Applications of Matrix Addition and Subtraction The applications of addition and subtraction of matrices can be illustrated through the following examples: - 5 - 2969 3214 7542 2314 2876 2000 1 1 3 4 2 11 18 15 16 19 11 26 22 14 17 12 13

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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 –
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