Question

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

Answer 1

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

`(-13,16)`

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)

`(color(red)((-5, 2))) xx((color(blue)(1), color(orange)(-2)), (color(blue)(-4), color(orange)( 3)))`

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

`(color(red)("red row")xxcolor(blue)("blue column")" "color(red)("red row")xxcolor(orange)("orange column"))`

=`(-5xx1+2xx-4" "-5xx-2 +2xx3)`

`(-13,16)`