Determine: begin{bmatrix}1 & -1 & 2 end{bmatrix}left{ begin{bmatrix}4 -1 0 end{bmatrix} begin{bmatrix}2 & 3 end{bmatrix}+begin{bmatrix}1 & 0 0 & 1-1&-1 end{bmatrix}right}

Determine:
$\left[\begin{array}{ccc}1& -1& 2\end{array}\right]\left\{\left[\begin{array}{c}4\\ -1\\ 0\end{array}\right]\left[\begin{array}{cc}2& 3\end{array}\right]+\left[\begin{array}{cc}1& 0\\ 0& 1\\ -1& -1\end{array}\right]\right\}$
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Step 1
$\left[\begin{array}{ccc}1& -1& 2\end{array}\right]\left\{\left[\begin{array}{c}4\\ -1\\ 0\end{array}\right]\left[\begin{array}{cc}2& 3\end{array}\right]+\left[\begin{array}{cc}1& 0\\ 0& 1\\ -1& -1\end{array}\right]\right\}$
$=\left[\begin{array}{ccc}1& -1& 2\end{array}\right]\left\{\left[\begin{array}{cc}8& 12\\ -2& -3\\ 0& 0\end{array}\right]+\left[\begin{array}{cc}1& 0\\ 0& 1\\ -1& -1\end{array}\right]\right\}$
$=\left[\begin{array}{ccc}1& -1& 2\end{array}\right]\left[\begin{array}{cc}9& 12\\ -2& -2\\ -1& -1\end{array}\right]$
Step 2
$=\left[\begin{array}{ccc}1& -1& 2\end{array}\right]\left[\begin{array}{cc}9& 12\\ -2& -2\\ -1& -1\end{array}\right]$
$=\left[\begin{array}{cc}\left(9+2-2\right)& \left(12+2-2\right)\end{array}\right]$
$=\left[\begin{array}{cc}9& 12\end{array}\right]$