1. Warm-Up 3) 1)
4) Name the dimensions 2)

2. Answers

3. Quiz – you may not use your notes1) 3)
4) Name the dimensions 2)
Check your work!! Watch out for careless errors.

4. 3.6 Multiplying Matrices
Algebra II

5. In order to multiply matrices...
A • B = AB
m x n
n x p
m x p
Ex 1.
Can you multiply? What will the dimensions be? A B AB
2 x 3
3 x 4
2 x 4 AB A B
5 x 3
5 x 2
Not possible

6. If we are multiplying matrices, we multiply each row of the first matrix by each column in the second matrix!!

7. How to multiply... ac ad =
2 x 1
1 x 2
2 x 2

8. How to multiply... ac ad = bc bd
2 x 1
1 x 2
2 x 2

9. Ex. 1

10. Ex. 2
Find AB
-16
+ 1
-12 +2
-15
-10 =
- 2
- 4 -2
- 4

11. Ex. 3
Find BA

12. How to multiply... ag
+bi
+ck ah
+bj
+cm =
2 x 3
3 x 2
2 x 2

13. 2 x 3 3 x 2 2 x 2 = How to multiply... ag +bi +ck ah +bj +cm dg +ei
+fk dh
+ej
+fm
2 x 3
3 x 2
2 x 2

14. Ex. 4 -1(4) +5(6) -1(-3) +5(8) -4 + 30 3 + 40 5(4) +2(6) 5(-3) +2(8)20
+12
-15
+ 16 =
+ -24
+ -32
0(4)
+-4(6)
0(-3)
+-4(8) 26 43 32 1
-24
-32

15. If we are multiplying matrices, we multiply each row of the first matrix by each column in the second matrix!!
multiply each row of the first matrix by each column in the second matrix!! + + 1 + + 2 + + 1 + +

16. 2 X 3 3 X 3 2(3)+(-3)(8)+5(-3) 2(9)+(-3)(0)+ 5(1) 2(1)+(-3)(-4)+ 5(5)
-1(3)+(6)(8)+8(-3)
-1(9)+(6)(0)+ 8(1)
-1(1)+(6)(-4)+ 8(5)

17. Ex. 5

18. Any questions?

19. Assignment