And because these two matrices

are not of the same dimension,

you know, this is an error,

so you cannot add these

two matrices and, you know,

their sum is not well-defined.

So that's matrix addition.

Next, let's talk about multiplying matrices by a scalar number.

And the scalar is just a,

maybe a overly fancy term for,

you know, a number or a real number.

Alright, this means real number.

So let's take the number 3 and multiply it by this matrix.

And if you do that, the result is pretty much what you'll expect.

You just take your elements

of the matrix and multiply

them by 3, one at a time.

So, you know, one

times three is three.

What, two times three is

six, 3 times 3

is 9, and let's see, I'm

going to stop changing colors again.

Zero times 3 is zero.

Three times 5 is 15, and 3 times 1 is three.

And so this matrix is the

result of multiplying that matrix on the left by 3.

And you notice, again,

this is a 3 by 2

matrix and the result is

a matrix of the same dimension.

This is a 3 by

2, both of these are

3 by 2 dimensional matrices.

And by the way,

you can write multiplication, you know, either way.

So, I have three times this matrix.

I could also have written this

matrix and 0, 2, 5, 3, 1, right.

I just copied this matrix over to the right.

I can also take this matrix and multiply this by three.

So whether it's you know, 3

times the matrix or the

matrix times three is

the same thing and this thing here in the middle is the result.