# How do you multiply ((1, -2), (-4, 3)) with ((-5, 2))?

Aug 24, 2016

These matrices are not compatible and cannot be multiplied.
They can only be multiplied the other way round to give:

$\left(- 13 , 16\right)$

#### Explanation:

These matrices are not compatible as they are shown.

A (2x2) matrix cannot multiply by a (1x2) matrix.

But, a (1x2) matrix can multiply by a (2x2) matrix to give a (1x2)

$\left(\textcolor{red}{\left(- 5 , 2\right)}\right) \times \left(\begin{matrix}\textcolor{b l u e}{1} & \textcolor{\mathmr{and} a n \ge}{- 2} \\ \textcolor{b l u e}{- 4} & \textcolor{\mathmr{and} a n \ge}{3}\end{matrix}\right)$

The red row must multiply by each of the columns in the second matrix.

$\left(\textcolor{red}{\text{red row")xxcolor(blue)("blue column")" "color(red)("red row")xxcolor(orange)("orange column}}\right)$

=$\left(- 5 \times 1 + 2 \times - 4 \text{ } - 5 \times - 2 + 2 \times 3\right)$

$\left(- 13 , 16\right)$