#### Please solve RD Sharma class 12 chapter Algebra of matrices exercise 4.3 question 76 maths textbook solution

Answer: The total requirements of calories and proteins for the two families are  $\left[\begin{array}{ll} 24600 & 576 \\ 15800 & 332 \end{array}\right]$

Hint: Matrix multiplication is only possible, when the number of columns of first matrix is equal to the number of rows of second matrix.

Given: Two families A and B there are 4 men, 6 women and 2 children in family A, 2 men, women and 4 children in family B.

Daily amount of calories is 2400 for men, 1900 for women, and 1800 for children. 45 grams of protein for men and 55 grams for women and 33 grams for children.

Let F be the family matrix and R be the requirements matrix.

Then,

$\\F= \begin{array}{c}A \\ B \end{array} \left[\begin{array}{lll}4 & 6 & 2 \\ 2 & 2 & 4\end{array}\right] \\\\ R=\begin{array}{c}M \\ W \\ C\end{array}\left[\begin{array}{cc}2400 & 45 \\ 1900 & 55 \\ 1800 & 33\end{array}\right]$

The requirement of calories and proteins of each of the two families is given by the product matrix FR, as matrix F has number of columns equal to number of rows of R thus

$\\F R=\left[\begin{array}{lll}4 & 6 & 2 \\ 2 & 2 & 4\end{array}\right]\left[\begin{array}{ll}2400 & 45 \\ 1900 & 55 \\ 1800 & 33\end{array}\right] \\\\\\ F R=\left[\begin{array}{lc}4 \times 2400+6 \times 1900+2 \times 1800 & 4 \times 45+6 \times 55+2 \times 33 \\ 2 \times 2400+2 \times 1900+4 \times 1800 & 2 \times \times \times 45+2 \times 55+4 \times 33\end{array}\right]\\\\\\ F R=\begin{array}{l}A \\ B\end{array}\left[\begin{array}{ll}24600 & 576 \\ 15800 & 332\end{array}\right]$

We can say that a balanced diet having the required amount of calories and proteins must be taken by each of the family members.