1. Matrix Multiplication
Honors Trig
Matrix Multiplication

2. # of columns in A = # of rows in B
Definition:
Suppose A is an m x n matrix and B is an n x p matrix. The product AB, (or AB) is defined as the m x p matrix whose element in row k and column j is the product of row k of A and column j of B.
# of columns in A = # of rows in B
Result has # of rows from A and # of columns from B
Students should record this definition. When doing the next few examples, refer to the definition in calculating the new dimensions of the product matrix.

3. Can the following matrices be multiplied?
Yes!
MATCH
3 X 1
1 X 3
Results is a 3 X 3 matrix.

4. Can the following matrices be multiplied?
NO!
DON’T MATCH
3 X 2
3 X 2

5. Consider the matrices below.
AB =
2 X 3
Results in a 3 X 3 matrix.
3 X 2
MATCH

6. 2 3 9 8 7 5 4 6 5 4 7 6
2(9)+3(6)
The next several slides are automatically animated. (NO CLICKING). Emphasize that this multiplication is row by column and how the rows and columns must align. I have color coordinated the row in the first matrix with the resulting row in the resulting matrix.

7. 2 3 9 8 7 5 4 6 5 4 7 6
2(9)+3(6)
2(8)+ 3(5)

8. 2 3 9 8 7 5 4 6 5 4 7 6
2(9)+3(6)
2(8)+ 3(5)
2(7)+ 3(4)

9. 2 3 9 8 7 5 4 6 5 4 7 6
2(9)+3(6)
2(8)+ 3(5)
2(7)+ 3(4)
4(9)+5(6)

10. 2 3 9 8 7 5 4 6 5 4 7 6
2(9)+3(6)
2(8)+ 3(5)
2(7)+ 3(4)
4(9)+5(6)
4(8)+ 5(5)

11. 2 3 9 8 7 5 4 6 5 4 7 6
2(9)+3(6)
2(8)+ 3(5)
2(7)+ 3(4)
4(9)+5(6)
4(8)+ 5(5)
4(7)+ 5(4)

12. 2 3 9 8 7 5 4 6 5 4 7 6
2(9)+3(6)
2(8)+ 3(5)
2(7)+ 3(4)
4(9)+5(6)
4(8)+ 5(5)
4(7)+ 5(4)
6(9)+7(6)

13. 2 3 9 8 7 5 4 6 5 4 7 6
2(9)+3(6)
2(8)+ 3(5)
2(7)+ 3(4)
4(9)+5(6)
4(8)+ 5(5)
4(7)+ 5(4)
6(9)+7(6)
6(8)+ 7(5)

14. 2 3 9 8 7 5 4 6 5 4 7 6
2(9)+3(6)
2(8)+ 3(5)
2(7)+ 3(4)
4(9)+5(6)
4(8)+ 5(5)
4(7)+ 5(4)
6(9)+7(6)
6(8)+ 7(5)
6(7)+ 7(4)

15. 2(9)+3(6)
2(8)+ 3(5)
2(7)+ 3(4)
4(9)+5(6)
4(8)+ 5(5)
4(7)+ 5(4)
6(9)+7(6)
6(8)+ 7(5)
6(7)+ 7(4) 36 31 26 66 57 48 96 83 70

16. Try this one:

18. Solution:

19. End of Day 1
Homework: Please complete the “Operations with Matrices WS” for homework!
Have an excellent day.

20. multiply by hand as well!!!
How to use
the calculator...
*You need to know how to
multiply by hand as well!!!

21. Find and press the matrix key on the calculator.
Using the TI-84
Find and press the matrix key on the calculator.

22. Find and press the matrix key on the calculator.
Using the TI-84
Find and press the matrix key on the calculator.

23. Arrow across to highlight edit.
Using the TI-84
Arrow across to highlight edit.

24. Arrow across to highlight edit.
Using the TI-84
Arrow across to highlight edit.

25. Using the TI-84
Matrix Dimensions
Column
Row

26. Enter the matrices Example 3 into A and B
Using the TI-84
Enter the matrices Example 3 into A and B

27. Enter the matrices Example 3 into A and B
Using the TI-84
Enter the matrices Example 3 into A and B

28. Multiply the two matrices.
Using the TI-84
Multiply the two matrices.
Press MATRX and select matrix A, press , then press MATRX and select matrix B.

29. Multiply the two matrices.
Using the TI-84
Multiply the two matrices.
Press MATRX and select matrix A, press , then press MATRX and select matrix B.