Warm-Up

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

2. Quiz – you may not use your notes 1) 3) 4) Name the dimensions 2) Check your work!! Watch out for careless errors.

3. 4.3 Multiplying Matrices “take it row by column”

4. In order to multiply matrices... A • B = AB m xn m x p nx 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

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

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

7. Ex. 1

8. Ex. 2 FindAB -16 + 1 -12 +2 -15 -10 = 0 - 2 0 - 4 -2 - 4

9. Ex. 3 FindBA – be careful, order matters

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

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

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

13. 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 + +

14. 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)

15. Ex. 5

16. What are your questions? OK … time to use your knowledge!