Question

Use the following matrices to evaluate the given expression.

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

role="math" localid="1647454108124" $CA$

Short answer

$CA=\left[\begin{array}{ccc}1& 14& -14\\ 2& 22& -18\\ 3& 0& 28\end{array}\right]$

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

$$\begin{gathered} A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right],C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right] \\ CA=\left[\begin{array}{ccc}4\times 0+1\times 1& 4\times 3+1\times 2& 4(-5)+1\times 6\\ 6\times 0+2\times 1& 6\times 3+2\times 2& 6(-5)+2\times 6\\ (-2)\times 0+3\times 1& (-2)\times 3+3\times 2& (-2)(-5)+3\times 6\end{array}\right] \\ CA=\left[\begin{array}{ccc}1& 14& -14\\ 2& 22& -18\\ 3& 0& 28\end{array}\right] \end{gathered}$$