3.6 – Multiply MatricesThe product of two matrices A and B is

defined provided the number of columns in A is equal to the number of rows in B.

If A is an m x n matrix and B is an n x p matrix, then the product AB is an m x p matrix.

3.6 – Multiply MatricesExample 1:

State whether the product of AB is defined. If so, give the dimensions of AB.

a. A: 4x3, B: 3x2 b. A: 3x4, B: 3x2

c. A: 3x5, B:5x2 d. A: 3x4, B: 3x2

3.6 – Multiply Matrices

3.6 – Multiply MatricesExample 2:

3.6 – Multiply MatricesExample 3:

3.6 – Multiply MatricesExample 4:

Using the given matrices, evaluate the expression.

a. A(B +C) b. AB + BC

3.6 – Multiply Matrices

3.6 – Multiply MatricesExample 5:

Two hockey teams submit equipment lists for the season as shown. Each stick costs $60, each puck costs $2, and each uniform costs $35. Use matrix multiplication to find the total cost of equipment for

each team.