In a city there are two factories A and B. Each factory produces sports clothes for boys and girls. There are three types of clothes produced in both the factories type I, II and III are 80. 70 and 65 in factory A and 85, 65 and 72 in factory B. For girls the number of units of I, II and III are 80, 75.90 in factory A and 50, 55, 80 in factory B. Express this information in terms of matrices and using matrix algebra answer the following questions.
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(1) Total units of type I produced for boys = a11 + b11
= 80 + 85 = 165
(2) Total production of each type for boys = a11 + a12 + a13 + b11 + b12 + b13
= 80 + 70 + 65 + 85 + 65 + 72 = 437
(3) Total production of each type for girls = a21 + a22 + a23 + b21 + b22 + b23
= 80 + 75 + 90 + 50 + 55 + 80 = 430
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