Chapter 9, Problem 46RE

Matrix $M$ gives the manufacturer price for four models of dining room tables. Matrix $P$ gives the retail price to the customer.

$\begin{array}{l}\begin{array}{cc}\text{Wood}& \text{Metal}\end{array}\\ M=\left[\begin{array}{cc}\$1050& \$940\\ \$890& \$800\end{array}\right]\begin{array}{c}\text{Large}\\ \text{Small}\end{array}\end{array}$

$\begin{array}{l}\begin{array}{cc}\text{Wood}& \text{Metal}\end{array}\\ P=\left[\begin{array}{cc}\$1365& \$1222\\ \$1157& \$1040\end{array}\right]\begin{array}{c}\text{Large}\\ \text{Small}\end{array}\end{array}$

a. Compute $P-M$ and interpret its meaning.

b. if the tax rate in a certain city is $6\%$ , use scalar multiplication to find a matrix $F$ that gives the final price (including sales tax) to the for each model.