Chapter 2.5, Problem 67E

DIET PLANNING A dietician plans a meal around three foods. The number of units of vitamin A, Vitamin C and calcium in each ounce of these foods is represented by the matrix $M$, where,

$\begin{array}{l}\text{Food}\\ \text{I}\text{II}\text{III}\\ M=\begin{array}{c}\text{Vitamin}\text{A}\\ \text{Vitamin}\text{C}\\ \text{Calcium}\end{array}\left[\begin{array}{ccc}400& 1200& 800\\ 110& 570& 340\\ 90& 30& 60\end{array}\right]\end{array}$

The matrices $A$ and $B$ represents the amount of each food (in ounces) consumed by a girl at two different meals, where,

$\begin{array}{l}\text{Food}\\ \text{I}\text{II}\text{III}\\ A=\left[\begin{array}{ccc}7& 1& 6\end{array}\right]\end{array}$

And

$\begin{array}{l}\text{Food}\\ \text{I}\text{II}\text{III}\\ B=\left[\begin{array}{ccc}9& 3& 2\end{array}\right]\end{array}$

Calculate the following matrices, and explain the meaning of entries in each matrix.

a. $M{A}^T$

b. $M{B}^T$

c. $M{\left(A+B\right)}^T$