Answer
See explanation
Work Step by Step
Put vector $u=\left[\begin{array}{l}S \\ C\end{array}\right]$ represents the amounts of Shredded Wheat and Crispix
Nutrient vectors for Shredded Wheat and Crispix are:
$v_{1}=\left[\begin{array}{c}160 \\ 5 \\ 6 \\ 1\end{array}\right]$ and $v_{2}=\left[\begin{array}{c}110 \\ 2 \\ .1 \\ .4\end{array}\right]$
a)
\[
\text { put} B=\left[\begin{array}{ll}
v_{1} & v_{2}
\end{array}\right] \text { and } u=\left[\begin{array}{l}
3 \\
2
\end{array}\right]
\]
Then $B u$ lists the amounts of calories, protein, carbohydrate and fat in mixture of three servings of Shredded Wheat and two servings of Crispix.
Note that we are multiplying $4 \times 2$ with $2 \times 1$ matrix, meaning that the resulting matrix will be $4 \times 1$ matrix which corresponds to nutrient vector for a mixture.
b)
Let $S$ and $C$ in vector $u$ represent the number of servings of Shredded Wheat and Crispix.
We should solve following matrix equation:
$B u=\left[\begin{array}{c}130 \\ 3.2 \\ 2.46 \\ .64\end{array}\right]$
Put augmented matrix for this equation and row reduce it using Matlab's function $\operatorname{rref}(A)$
$\left[\begin{array}{cc|c}160 & 110 & 130 \\ 5 & 2 & 3.2 \\ 6 & .1 & 2.46 \\ 1 & .4 & .64\end{array}\right] \sim\left[\begin{array}{cc|c}1 & 0 & .4 \\ 0 & 1 & .6 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]$
We should mix .4 servings of Shredded Wheat and .6 servings of Crispix for desired nutrients.
