Ramkishan Gurcharan Singh Thus in October Ramkishan receives 100 200 and 120 as profit in the sale of each variety of rice respectively and Grucharan Singh receives profit of 400 200 and 200 in the sale of each variety of rice respectively 5 8 10 11 100 400 3 4 5 Multiplication of matrices Suppose Meera and Nadeem are two friends Meera wants to buy 2 pens and 5 story books while Nadeem needs 8 pens and 10 story books They both go to a shop to enquire about the rates which are quoted as follows Pen 5 each story book 50 each How much money does each need to spend Clearly Meera needs 5 2 50 5 that is 260 while Nadeem needs 8 x 5 50 10 that is 540 In terms of matrix representation we can write the above information as follows Requirements Prices per piece in Rupees Money needed in Rupees 260 5 50x50 340 50 200 200 2 5 8 10 2 5 8 10 120 200 Suppose that they enquire about the rates from another shop quoted as follows pen 4 each story book 40 each de f Now the money required by Meera and Nadeem to make purchases will be respectively 4 2 40 5 208 and 8 4 10 40 432 Rationalised 2023 24 4 40 5x2 5x50 8x5 10x50 5 4 50 40 Again the above information can be represented as follows Requirements Prices per piece in Rupees Money needed in Rupees MATRICES 51 Now the information in both the cases can be combined and expressed in terms of matrices as follows Requirements Prices per piece in Rupees Money needed in Rupees 208 8 4 10 40 432 260 208 5x2 5x50 4x2 40 5 8x5 10x50 8 4 10 40 The above is an example of multiplication of matrices We observe that for multiplication of two matrices A and B the number of columns in A should be equal to the number of rows in B Furthermore for getting the elements of the product matrix we take rows of A and columns of B multiply them element wise and take the sum Formally we define multiplication of matrices as follows HOUT The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B Let A a be an m n matrix and B b be an nxp matrix Then the product of the matrices A and B is the matrix C of order m p To get the i k th element c of the matrix C we take the ith row of A and kth column of B multiply them elementwise and take the sum of all these products In other words if A almx B bl xp then the ith row of A is a a a and the kth column of