Compute the indicated products: 1&-2 2&3 1&2&3 -3&2&-1 - Vidyadip

Question

Compute the indicated products:
$\begin{bmatrix}1&-2\\2&3\end{bmatrix}\begin{bmatrix}1&2&3\\-3&2&-1\end{bmatrix}$

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Answer

$\begin{bmatrix}1&-2\\2&3\end{bmatrix}\begin{bmatrix}1&2&3\\-3&2&-1\end{bmatrix}$
$=\begin{bmatrix}(1)(1)+(-2)(-3)&(1)(2)+(-2)(2)&(1)(3)+(-2)(1)\$2)(1)+(3)(-3)&(2)(2)+(3)(2)&(2)(3)+(3)(-1)\end{bmatrix}$
$=\begin{bmatrix}1+6&2-4&3+2\\2-9&4+6&6-3\end{bmatrix}$
$=\begin{bmatrix}7&-2&5\\-7&10&3\end{bmatrix}$

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