Matrices Multiplication Assume that matrix A is of

Matrices - Multiplication • Assume that matrix A is of order m n and matrix B is of order p q. To determine whether or not A can be multiplied times B, write the matrices with their orders. . . A m n B p q. • If the two inside numbers are the same, then matrix multiplication is possible. • When multiplication is possible, the resulting matrix will have an order determined by the outside numbers. Table of Contents

Matrices - Multiplication • Example 1: Find AB where A and B are given by. . . 2 3 3 4 • Since the inside numbers are the same, the multiplication is possible. • The resulting matrix will be 2 4. Table of Contents Slide 2

Matrices - Multiplication • The process of multiplying is as follows: • Multiply row 1 of matrix A times column 1 of matrix B. Table of Contents • To get the first entry of the product matrix, note that it is the row 1 column 1 entry. 2 4 Slide 3

Matrices - Multiplication • Multiply pairs of numbers by moving across the row and down the column, and add the products. (1)(1) + (-2)(3) + (3)(-2) = 1 - 6 6 = -11 Table of Contents Slide 4

Matrices - Multiplication • The next entry of the product matrix is in row 1 and column 2. • Multiplying as before with row 1 of matrix A and column 2 of matrix B. . . (1)(0) + (-2) + (3)(-1) = 1 Table of Contents Slide 5

Matrices - Multiplication The row 1 column 3 entry is. . . The row 1 column 4 entry is. . . The row 2 column 1 entry is. . . The row 2 column 2 entry is. . . The row 2 column 3 entry is. . . The row 2 column 4 entry is. . . Table of Contents Slide 6

Matrices - Multiplication • Thus, the product of the matrices is. . . Table of Contents Slide 7

Matrices - Multiplication • Example 2: Find CD where C and D are given by. . . • The answer is. . . Table of Contents Slide 8

Matrices - Multiplication Table of Contents