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.
1.Total units of type $I$ produced for boys?
2.Total production of each type for boys?
3.Total production of each type for girls?

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Solution

Let the first and second row represents the clothes produced for boys and girls respectively.
Let the first, second and third column represents the clothes produced of $I, I I$ and $I I I$ respectively.
$A = ∣ ∣ ∣ \begin{matrix} 80 & 70 & 65 80 & 75 & 90 \end{matrix} ∣ ∣ ∣$
$B = ∣ ∣ ∣ \begin{matrix} 85 & 65 & 72 50 & 55 & 80 \end{matrix} ∣ ∣ ∣$
Now, from th above two matrices-
Total units of type $I$ produced for boys $= a_{11} + b_{11} = 80 + 85 = 165$
Total production of each type for boys $= a_{11} + a_{12} + a_{13} + b_{11} + b_{12} + b_{13} = 80 + 70 + 65 + 85 + 65 + 72 = 437$
Total production of each type for girls $= a_{21} + a_{22} + a_{23} + b_{21} + b_{22} + b_{23} = 80 + 75 + 90 + 50 + 55 + 80 = 430$

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