Question

Use the following matrices to evaluate the given expression.

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

$-3B$

Short answer

-$-3B=\left[\begin{array}{ccc}-12& -3& 0\\ 6& -9& 6\end{array}\right]$

Step-by-step solution

Step 1. Given Information

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

Step 2. Calculation

$$\begin{gathered} -3B=-3\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right] \\ =\left[\begin{array}{ccc}-12& -3& 0\\ 6& -9& 6\end{array}\right] \end{gathered}$$