# How do you multiply the matrices ((2, 3), (1, -3)) with ((-1, 0, 2), (0, 2, 3))?

Mar 24, 2016

$\left(\begin{matrix}- 2 & 6 & 13 \\ - 1 & - 6 & - 7\end{matrix}\right)$

#### Explanation:

Remember when multiplying matrices each entry in the product matrix are form by the corresponding
$\textcolor{w h i t e}{\text{XXX}}$row from the first matrix, and
$\textcolor{w h i t e}{\text{XXX}}$column from the second matrix

$\left(\begin{matrix}\textcolor{red}{2} & \textcolor{red}{3} \\ \textcolor{b l u e}{1} & \textcolor{b l u e}{- 3}\end{matrix}\right) \times \left(\begin{matrix}\textcolor{b r o w n}{- 1} & \textcolor{c y a n}{0} & \textcolor{\mathmr{and} a n \ge}{2} \\ \textcolor{b r o w n}{0} & \textcolor{c y a n}{2} & \textcolor{\mathmr{and} a n \ge}{3}\end{matrix}\right)$

=( (color(red)(2)(color(brown)(-1))+color(red)(3)(color(brown)(0)), color(red)(2)(color(cyan)(0))+color(red)(3)(color(cyan)(2)), color(red)(2)(color(orange)(2))+color(red)(3)(color(orange)(3))), (color(blue)(1)(color(brown)(-1))+(color(blue)(-3))(color(brown)(0)),color(blue)(1)(color(cyan)(0))+(color(blue)(-3))(color(cyan)(2)),color(blue)(1)(color(orange)(2))+(color(blue)(-3))(color(orange)(3))) )

$= \left(\begin{matrix}- 2 & 6 & 13 \\ - 1 & - 6 & - 7\end{matrix}\right)$