Multiplying Matrices

Algebra 2—Section 3.6

**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.

3 2 57 1 0

8 21 50 3

Dimensions (order): 3 x 22 x 3

These must match.

These give the dimensions (order) of your answer.

3 9 2 2 1

5 7 6 3 4

Dimensions (order): 2 x 3 2 x 2*They don’t match so these cannot be multiplied together.*

Multiply.Can these be multiplied?Check the order of each!

Examples:2 1 3 9 2

3 4 5 7 6

2(3) + -1(5) 2(-9) + -1(7) 2(2) + -1(-6)

3(3) + 4(5) 3(-9) + 4(7) 3(2) + 4(-6)

1 25 1029 1 18

Can these be multiplied?Check the order of each!

Now multiply each row of the 1st matrix by each column of the 2nd matrix

Yes, they can!!

0 1 4 3

1 0 2 5

2 x 2 2 x 2

*Answer should be a 2 x 2

0(4) + (-1)(-2) 0(-3) + (-1)(5)

1(4) + 0(-2) 1(-3) + 0(5)

2 -54 -3

Multiply.

1 3 02 12 4

9 14 32 4

21 874 50

Multiply.

On a side note:

1 2 1 1 1 3 2 7

2 6 1 8

xyz

x 2y z 1x 3y 2z 72x 6y z 8

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 columnMultiply them line by line

Add the products for an entryNow you’re doing it just fine

Homework: p. 199-200 #6-15 multiples of 3,

#20, 22, 30