Chapter 2.3, Problem 75E

Nutrition Analysis Mikey’s diet consists of food X and food Y. The matrix N represents the number of units of nutrients 1, 2, and 3 per ounce for each of the foods.

$\begin{array}{l}123\\ N=\left[\begin{array}{ccc}60& 50& 38\\ 42& 50& 67\end{array}\right]\begin{array}{c}X\\ Y\end{array}\end{array}$

The matrices B, L, and D represent the number of ounces of each food that Mikey eats each day for breakfast, lunch, and dinner, respectively.

$\begin{array}{l}\begin{array}{cc}X& Y\end{array}\begin{array}{cc}X& Y\end{array}\begin{array}{cc}X& Y\end{array}\\ B=\left[\begin{array}{cc}2& 1\end{array}\right]L=\left[\begin{array}{cc}1& 3\end{array}\right]D=\left[\begin{array}{cc}2& 4\end{array}\right]\end{array}$

Calculate and interpret the following:

(a) $BN$

(b) $LN$

(c) $DN$

(d) $B+L+D$

(e) $\left(B+L+D\right)N$