1. Objectives: Students will be able to… Multiply two matrices Apply matrix multiplication to real life problems.

2. Multiplying 2 Matrices The # of columns in 1 st matrix MUST EQUAL the # of rows in the 2 nd matrix: 3 x 2 2 x 2 MUST BE EQUAL!!! The product matrix will have the dimensions 3 X 2

3. State whether the product matrix is defined. If so, give its dimensions. a.) A: 2 X 4B: 4 X 3 b.) A: 1 X 4 B: 1 X 4

4. Finding the product:

5. Example:

6. Find each product: AB:BA:

7. Properties of Matrix Multiplication: A, B, and C are matrices, c is a scalar Associative Property of Matrix: A(BC) = (AB)C Left Distributive: A(B + C) = AB + AC Right Distributive: (A + B)C = AC + BC Associative Property of Scalar: c(AB) = (cA)(B) = A(cB)

8. Examples: Find: a.) B(A +C)b.) BA + BC

9. Example: Find A(BC)

10. Total Cost Matrix Inventory X Cost per item= Total Cost Matrix Matrix Matrix m X n n X p m X p

11. Two Lacrosse teams submit equipment lists to their sponsors. Women’s team: 5 sticks, 15 balls, and 16 uniforms. Men’s team: 8 sticks, 22 balls, and 17 uniforms. Each stick costs $55, each ball costs $6, and each uniform costs $35. Use matrix multiplication to find total cost of equipment for each team.