90 70 75 Suppose Fatima wants to know the total production of sport shoes in each price category Then the total production In category 1 for boys 80 90 for girls 60 50 In category 2 for boys 75 70 for girls 65 55 In category 3 for boys 90 75 for girls 85 75 80 90 This can be represented in the matrix form as 75 70 90 75 1 2 3 44 MATHEMATICS 80 75 90 60 65 85 911 912 913 Thus if A 921 922 923 1 2 3 Rationalised 2023 24 Example 6 Given A This new matrix is the sum of the above two matrices We observe that the sum of two matrices is a matrix obtained by adding the corresponding elements of the given matrices Furthermore the two matrices have to be of the same order 2x3 matrix Then we define A B is a 2 3 matrix and B 31 2 3 0 a b a 2 b 2 a21 b 1 a22 b 2 and B 50 55 75 2 5 60 50 65 55 85 75 2 3 In general if A a and B b are two matrices of the same order say m n 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 where b b2 b13 b21 b2 a 3 b 3 a23 b 3 b23 is another 45 Since A B are of the same order 3 Therefore addition of A and B is defined and is given by 12 55 1 255 1 1 2 6 1 1 5 07