Let's look at just one more example.

Let's say I want to multiply together these two matrices.

So what I'm going to do is first pull out the first column of my second matrix.

That was my matrix B on the previous slide and

I therefore have this matrix times that vector.

And so, oh, let's do this calculation quickly.

This is going to be equal to the 1, 3 x 0,

3, so that gives 1 x 0 + 3 x 3.

And the second element is going to be 2, 5 x 0,

3, so that's gonna be 2 x 0 + 5 x 3.

And that is 9, 15.

Oh, actually let me write that in green.

So this is 9, 15.

And then next I'm going to pull out the second column of this and

do the corresponding calculations.

So that's this matrix times this vector 1, 2.

Let's also do this quickly, so

that's 1 x 1 + 3 x 2, so that was that row.

And let's do the other one.

So let's see,

that gives me 2 x 1 + 5 x 2 and

so that is going to be equal to,

lets see, 1 x 1 + 3 x 1 is 7 and

2 x 1 + 5 x 2 is 12.

So now I have these two and so my outcome,

the product of these two matrices,

is going to be this goes here and this goes here.

So I get 9, 15 and

4, 12. [It should be 7,12]

And you may notice also that the result of multiplying a 2x2 matrix with another 2x2

matrix, the resulting dimension is going to be that first 2 times that second 2.

So the result is itself also a 2x2 matrix.