Question

How do you multiply `((3, 1, -2, 0), (1, 4, -2, -2), (-2, 0, 7, -3), (-1, 3, -1, 2))` with `((1, 1), (1, -2), (-3, 2), (4, 5))`?

Answer 1

`((3, 1, -2, 0), (1, 4, -2, -2), (-2, 0, 7, -3), (-1, 3, -1, 2))((1, 1), (1, -2), (-3, 2), (4, 5))=((10, -3),(3 , -21),(-35, -3),(13, 1))`

Explanation:

When we multiply matrices, we must first check that they're compatible for multiplication.

`((3, 1, -2, 0), (1, 4, -2, -2), (-2, 0, 7, -3), (-1, 3, -1, 2))` is `4xx4`

`((1, 1), (1, -2), (-3, 2), (4, 5))` is `4xx2`

So, they are compatible and the dimensions of the product are `4xx2`. Now, when we multiply matrices we do it by multiplying each row of the first matrix with each column of the second.

So,

`((3, 1, -2, 0), (1, 4, -2, -2), (-2, 0, 7, -3), (-1, 3, -1, 2))((1, 1), (1, -2), (-3, 2), (4, 5))=((10,-3),(3,-21),(-35,-3),(13,1))`