Section 1.2 – Matrix Multiplication
Exercises
Directions: You should try to solve each problem first, and then click "Reveal Answer" to check your answer. You can click "Watch Video" if you need help with a problem.
1. Suppose Dr. Whitfield owns a convenience store that sells gas. On Monday her store sold 1500 gallons of regular-unleaded, 1000 gallons of unleaded-plus, and 800 gallons of super- unleaded gasoline. If the price of gasoline on this day was $2.25 for regular-unleaded, $2.69 for unleaded-plus, and $3.19 for super-unleaded gasoline.
- Write the number of gallons of gasoline sold as a ROW matrix A and the price per gallon as a COLUMN matrix B.
- Use A and B to find the revenue earned by selling gasoline on Thursday at Dr. Whitfield’s store.
- \(\begin{array}{lccc} & \text{Regular Unleaded} & \text{Unleaded Plus} & \text{Super Unleaded}\\ A=\text{Whitfield's Store} & [ 1500 & 1000 & 800 ]\end{array}\)
\( B=\begin{array}{lc} & \text{Dollars (\$)} \\ \text{Regular Unleaded} & |2.25|\\ \text{Unleaded Plus} & |2.69| \\ \text{Super Unleaded} & | 3.19|\end{array}\)
- \(\begin{array}{lc} & \text{Dollars (\$)} \\ AB=\text{Whitfield's Store} & [8617]\end{array}\)
2. Given matrices A, B, C and D below, find the resulting matrices in parts a–d, if possible.
\[
A=\left[\begin{array}{ccc}
2 & 0 & -3\\
p & x & 4w
\end{array}\right]
\quad
B=\left[\begin{array}{ccc}
6 & -2 & 0\\
3 & 5 & 1
\end{array}\right]\]
\[
C=\left[\begin{array}{cccc}
4 & -3 & 1 & 0
\end{array}\right]
\quad
D=\left[\begin{array}{cc}
4 & -2\\
r & 0\\
5 & 8\\
10 & 2
\end{array}\right]\]
- \(CD\)
- \(AB\)
- \(AB^T\)
- \(AD\)
- \(DA\)
- \(CD=\left[\begin{array}{cc} 21-3r & 0\end{array}\right]\)
- Multiplying \(AB\) is not possible.
- \(AB^T=\left[ \begin{array}{cc} 12 & 3\\ 6p -2x & 3p+5x+4w\end{array}\right]\)
- Multiplying \(AD\) is not possible.
- \(DA=\left[\begin{array}{ccc} 8-2p & -2x & -12-8w\\ 2r & 0 & -3r \\ 10+8p & 8x & -15+32w\\ 20+2p & 2x & -30+8w\end{array}\right]\)