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

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Answer 1 · 2016-08-24T21:22:50

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

$(-13,16)$

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.

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

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

$(-13,16)$

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