1. Multiplying Matrices
Algebra 2—Section 3.6

2. 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…

3. **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.
Dimensions (order):
3 x 2
2 x 3
These give the dimensions (order) of your answer.

4. *They don’t match so these cannot be multiplied together.*
Multiply.
Can these be multiplied?
Check the order of each!
Dimensions (order): 2 x x 2
*They don’t match so these cannot be multiplied together.*

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

6. 2 x 2 2 x 2 *Answer should be a 2 x 2 0(4) + (-1)(-2) 0(-3) + (-1)(5)
Multiply.
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)

7. Multiply.

8. On a side note: We can use matrices to write a system of equations.
This is useful when solving augmented matrices.

9. 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 you’re doing it just fine

10. Homework: p
#6-15 multiples of 3,
#20, 22, 30