Question

Use the following matrices to evaluate the given expression.

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

Short answer

$CB=\left[\begin{array}{ccc}14& 7& -2\\ 20& 12& -4\\ -14& 7& -6\end{array}\right]$

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

$$\begin{gathered} B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right],C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right] \\ CB=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right] \\ =\left[\begin{array}{ccc}4\times 4+1\times (-2)& 4\times 1+1\times 3& 4\times 0+1\times (-2)\\ 6\times 4+2\times (-2)& 6\times 1+2\times 3& 6\times 0+2\times (-2)\\ (-2)\times 4+3\times (-2)& (-2)\times 1+3\times 3& (-2)\times 0+3\times (-2)\end{array}\right] \\ =\left[\begin{array}{ccc}14& 7& -2\\ 20& 12& -4\\ -14& 7& -6\end{array}\right] \end{gathered}$$