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Multiplying Matrices

Algebra 2Section 3.6

Recall Scalar Multiplication - each element in

a matrix is multiplied by a constant.

Multiplying one matrix by another has a few more

rules to follow

The product of two matrices is defined if the

number of columns in the 1st matrix is equal to

the number of rows in the 2nd matrix.

These must match.

These give the dimensions (order) of your answer.

Multiply.

Can these be multiplied? Check the order of each!

Dimensions (order) 2 x 3 2 x 2

They dont match so these cannot be multiplied

together.

Examples

Can these be multiplied? Check the order of each!

Yes, they can!!

Now multiply each row of the 1st matrix by each

column of the 2nd matrix

2(3) -1(5)

2(-9) -1(7)

2(2) -1(-6)

3(-9) 4(7)

3(2) 4(-6)

3(3) 4(5)

Multiply.

Answer should be a 2 x 2

0(4) (-1)(-2)

0(-3) (-1)(5)

1(4) 0(-2)

1(-3) 0(5)

Multiply.

On a side note

We can use matrices to write a system of

equations.

This is useful when solving augmented matrices.

Multiplying Matrices Song

- (to the tune of Oh my Darling, Clementine)
- Row by column, row by column
- Multiply them line by line
- Add the products for an entry
- Now youre doing it just fine

Homework

- p. 199-200
- 6-15 multiples of 3,
- 20, 22, 30