College Algebra, Chapter 7, Review Exercises, Section Review Exercises, Problem 26

Let

$\displaystyle B = \left[
\begin{array}{ccc}
1 & 2 & 4 \\
-2 & 1 & 0
\end{array}
\right]
\qquad
C = \left[
\begin{array}{cc}
\displaystyle \frac{1}{2} & 3 \\
2 & \displaystyle \frac{3}{2} \\
-2 & 1
\end{array}
\right]$

Carry out the indicated operation $5B - 2C$, or explain why it cannot be performed.

$\displaystyle 5B - 2C = 5 \left[
\begin{array}{ccc}
1 & 2 & 4 \\
-2 & 1 & 0
\end{array}
\right] - 2 \left[
\begin{array}{cc}
\displaystyle \frac{1}{2} & 3 \\
2 & \displaystyle \frac{3}{2} \\
-2 & 1
\end{array}
\right] = \left[ \begin{array}{ccc}
5 & 10 & 20 \\
-10 & 5 & 0
\end{array} \right] -
\left[ \begin{array}{cc}
1 & 6 \\
4 & 3 \\
-4 & 2
\end{array} \right]
$

$5B - 2C$ is undefined because we can't subtract matrices of different dimensions.