Then the sum of the two matrices A and B is defined as a matrix C c c a b for all possible values of i and j Example 6 Given A 1 3 she A B defined 1 5 1 1 1 5 and B KARN Since A B are of the same order 3 Therefore addition of A and B is defined and is given by 2 3 2 2 3 3 0 2 5 1 1 2 3 2 3 B Note 1 We emphasise that if A and B are not of the same order then A B is not xample if A 1 5 0 1 2 This can be represented in the matrix 6 10 Rationalised 2023 24 23 e 31 2 We may observe that addition of matrices is an example of binary operation on the set of matrices of the same order 3 4 2 Multiplication of a matrix by a scalar Now suppose that Fatima has doubled the production at a factory A in all categories refer to 3 4 1 Girls 60 65 85 where then A B is not defined Previously quantities in standard units produced by factory A were Boys 80 75 90 Revised quantities produced by factory A are as given below Boys Girls 1 2 80 2x 60 2 2x75 2 65 32x90 2x85 MATRICES 170 olshed 45 We observe that the new matrix is obtained by multiplying each element of the previous matrix by 2 In general we may define multiplication of a matrix by a scalar as follows if A a is a matrix and k is a scalar then kA is another matrix which is obtained by multiplying each element of A by the scalar k mx n