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))#?

1 Answer
Mar 23, 2018

#((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))#