College Algebra, Chapter 7, Review Exercises, Section Review Exercises, Problem 24

Let

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

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

$\displaystyle C - D = \left[ \begin{array}{cc}
\displaystyle \frac{1}{2} & 3 \\
2 & \displaystyle \frac{3}{2} \\
-2 & 1
\end{array} \right] - \left[ \begin{array}{cc}
1 & 4 \\
0 & -1 \\
2 & 0
\end{array} \right] = \left[ \begin{array}{cc}
\displaystyle \frac{1}{2} - 1 & 3-4 \\
2-0 & \displaystyle \frac{3}{2}-(-1) \\
-2-2 & 1-0
\end{array} \right] = \left[ \begin{array}{cc}
\displaystyle \frac{-1}{2} & -1 \\
2 & \displaystyle \frac{5}{2} \\
-4 & 1
\end{array} \right]$

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