matrix multiplication

Multiplying matrices with the same dimensions

In order to multiply a matrix the inner numbers have to be the same.

-For example a 2x3 and 3x3 would be possible but a 3x4 and 2x4 wouldn’t be possible.

The outer numbers would give you the answer’s dimensions.

-For example a 2x3 and 3x3 would give you a 2x3 matrix.

Solve by multiplication.

1. [ 4 3] [5]

[-1 -2] [1]

The dimensions of this matrix are 2x2 and 2x1. This means this matrix is possible to multiply. First you multiply the first row by the first column. So, 4(5)+3(1)=23. Then multiply the second row by the by the column. So, -1(5)+-2(1)=-7. So the answer would be [23]

[-7]

2. [-6] [-1 12]

[ 2] [ 0 -4]

This matrix cannot be multiplied because the dimensions are 2x1 and 2x2. The inner numbers are not the same which means they cannot be multiplied.