1. MATRIX MULTIPLICATION
MATRICES
MATRIX MULTIPLICATION

2. Matrix Multiplication
If A, B, and C are matrices and k is an integer, then matrix multiplication is:
Associative: A(BC) = (AB)C
Left Distributive: A(B+C) = AB+BC
Right Distributive: (A+B)C=AC +BC
Associative with Scalar Multiplication: k(AB) = (kA)B = A(kB)
It is not commutative: AB ≠ BA

3. Matrix Multiplication
You can multiply matrices only if the number of columns in the first matrix equals the number of rows in the second matrix.
2 columns
2 rows

4. Matrix Multiplication
Notice the dimensions of the matrices and their product.
Note that if it had been a 2x3●3x2, the result would have been a 2x2 matrix. Commutative does not work!
3 x 2
2 x 3
3 x 3 __ __ __ __

5. State Whether the Product is Defined for Matrices A and B
A: 3X6, B:6x2
AB is a 3x2 matrix and is defined!
A: 2X7, B: 1X7
AB is not defined!
A: 4X2, B: 2X5
AB is a 4x5 matrix and is defined!

6. Matrix Multiplication
So how do we multiply a matrix?
With a math note sheet telling us how!
Please write this down! 

7. Example

8. Matrix Multiplication

9. Matrix Multiplication
Another example:
3 x 2
2 x 1
3 x 1

10. Example

11. Continued…

12. Real Life Problem---Soccer
Two soccer teams submit equipment lists for the season as shown:
How much will the total equipment cost for each team?
Quick Goals
Costs
Uniforms
Balls
Balls JV
Quick Goals
Quick Goals
Varsity
Uniforms

13. Real Life Problem---Soccer