Question

use the given matrices to compute each

expression.

$$\begin{gathered} A=\left[\begin{array}{cc}1& -1\\ 0& -4\\ 3& -2\end{array}\right] \\ B=\left[\begin{array}{ccc}1& -2& 5\\ 0& 3& 1\end{array}\right] \\ C=\left[\begin{array}{cc}4& 6\\ 1& -3\\ -1& 8\end{array}\right] \end{gathered}$$

$A-3C$

Short answer

The evaluation of the expression would be

$A-3C=\left[\begin{array}{cc}-11& -19\\ -3& 5\\ 6& -22\end{array}\right]$

Step-by-step solution

Step 1. Given

$$\begin{gathered} A=\left[\begin{array}{cc}1& -1\\ 0& -4\\ 3& -2\end{array}\right] \\ B=\left[\begin{array}{ccc}1& -2& 5\\ 0& 3& 1\end{array}\right] \\ C=\left[\begin{array}{cc}4& 6\\ 1& -3\\ -1& 8\end{array}\right] \end{gathered}$$

Step 2. Calculation

$$\begin{gathered} A-3C=\left[\begin{array}{cc}1& -1\\ 0& -4\\ 3& -2\end{array}\right]-3\left[\begin{array}{cc}4& 6\\ 1& -3\\ -1& 8\end{array}\right] \\ =\left[\begin{array}{cc}-11& -19\\ -3& 5\\ 6& -22\end{array}\right] \end{gathered}$$