Warm-Up 4 minutes Give the dimensions of each matrix. 1) 2)

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Warm-Up 4 minutes Give the dimensions of each matrix. 1) 2) Identify the entry at each location of the matrix below. 3) b12 4) b21 5) b32 6) 3

4.2 Matrix Multiplication Objectives: Multiply two matrices Use matrix multiplication to solve mathematical and real-world problems

Matrix Multiplication A football team scores 5 touchdowns, 4 extra points, and 2 field goals. A touchdown is worth 6 points, an extra point is worth 1 point, and a field goal is worth 3 points. The final score is: (5 touchdowns)(6 pts) + (4 extra points)(1 pt) + (2 field goals)(3 pts) = 30 points + 4 points + 6 points = 40 points touchdowns extra points field goals point values total score 6 5 4 2 1 (5)(6) + (4)(1) + (2)(3) 3

Matrix Multiplication To multiply any two matrices, the inner dimensions must be the same. Then the outer dimensions become the dimensions of the resulting matrix. inner dimensions product dimensions 2 x 3 3 x 4 = 2 x 4 outer dimensions

Example 1 Find the product. 1 x 3 3 x 2 = 1 x 2 (2)(8) + (5)(0) + (0)(2) (2)(1) + (5)(4) + (0)(5)

Practice Let A = and B = Find AB and BA.

Homework p.229 #7-19 odds,25