Chapter 9.3, Problem 69PE

Matrix $D$ gives the dealer invoice prices for sedan and hatchback models of a car with manual transmission or automatic transmission. Matrix $M$ gives the MSRP (manufacturer's suggested retail price) for the cars.

$\begin{array}{l}\begin{array}{cc}\text{Sedan}& \text{Hatchback}\end{array}\\ D=\left[\begin{array}{cc}\text{\$}29,000& \text{\$}27,500\\ \text{\$}28,500& \text{\$}26,900\end{array}\right]\begin{array}{c}\text{Manual}\\ \text{Automatic}\end{array}\end{array}$

$\begin{array}{l}\begin{array}{cc}\text{Sedan}& \text{Hatchback}\end{array}\\ M=\left[\begin{array}{cc}\text{\$}32,600& \text{\$}29,900\\ \text{\$}31,900& \text{\$}28,900\end{array}\right]\begin{array}{c}\text{Manual}\\ \text{Automatic}\end{array}\end{array}$

a. Compute $M-D$ and interpret the result.

b. A buyer thinks that a fair price is $6\%$ above dealer invoice. Use scalar multiplication to determine a matrix $F$ that gives the fair price for these cars for each type of transmission.