3.6 Multiply Matrices

To multiply matrices the matrix on the left needs to have the same number of columns as rows of the one on the right, and the resulting matrix will have same number of rows as the one on the left and columns as the one on the right. 5 7 4 1 3 2 2 1 4 = (5)(2)+(7)(1)+(4)(4) = 10 + 7 + 16 = 33 (1)(2)+(3)(1)+(2)(4) 2 + 3 + 8 13 Equal 2 x 3 2 x 1 resulting matrix 3 x 1 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

Multiply the Matrix A and B [A] [B] 3 5 1 1 3 2 2 1 5 4 6 = (3)(2)+(5)(1)+(1)(5) (3)(4)+(5)(2)+(1)(6) (1)(2)+(3)(1)+(2)(5) (1)(4)+(3)(2)+(2)(6) Equal = 6 + 5 + 5 12 + 10 + 6 2 x 3 2 x 2 resulting matrix 3 x 2 2 + 3 + 10 4 + 6 + 12 16 28 15 22 =

Write the system of equations represented by each matrix equation: -3 6 7 1 x y = 15 -8 -3x + 6y = 15 7x + y = -8 5 9 -2 4 x y = 5x + 9y = 0 -2x + 4y = 5

2 x 3 3 x 3 What are the dimensions of Matrix A and Matrix B? Is it possible to multiply these matrices? Yes What is the dimension of the product matrix AB? 2 x 3 Find the product AB. 29 21 4 1 -10