3.6

1
3.6 Multiply Matrices

• The 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.

2
3.6 Multiply Matrices

• Example 1
• State whether the product of AB is defined. If
  so, give the dimensions of AB.
• A 4x3, B 3x2 b. A 3x4, B 3x2
• c. A 3x5, B5x2 d. A 3x4, B 3x2

3
3.6 Multiply Matrices
4
3.6 Multiply Matrices

• Example 2

5
3.6 Multiply Matrices

• Example 3

6
3.6 Multiply Matrices

• Example 4
• Using the given matrices, evaluate the
  expression.
• a. A(B C) b. AB BC

7
3.6 Multiply Matrices
8
3.6 Multiply Matrices

• Example 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.