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Support Fatiila has two latiunits at places A allu D Each factory products spont shoes for boys and girls in three different price categories labelled 1 2 and 3 The quantities produced by each factory are represented as matrices given below 44 Boys 80 75 90 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 MATHEMATICS Factory at A In general if A 2x3 matrix Then we define A B Girls 60 65 85 Example 6 Given A A B 9 1 912 913 Thus if A is a 2 x 3 matrix and B 921 922 923 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 Rationalised 2023 24 2 2 31 Since A B are of the same order and is given by 1 2 3 2 3 0 2 3 1 5 1 1 1 5 1 1 3 3 0 Factory at B Boys 90 70 75 Then the sum of the two matrices A and B is defined as a matrix C c a b for all possible values of i and j a and B b are two matrices of the same order say m n where defined For example if A a b a 2 b 2 a21 b 1 a22 b22 and B 2 5 1 2 3 B 1 0 2 3 Girls 50 55 75 60 50 65 55 85 75 2 3 1 5 0 1 0 2 6 b b 2 b13 b 1 b22 b 3 a 3 b 3 a23 b 3 1 2 3 1 10 1 Therefore addition of A and B is defined is another Note 1 We emphasise that if A and B are not of the same order then A B is not use then A B is not defined

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