Table of Contents 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.

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

Table of Contents Slide 4 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) = = -11

Table of Contents Slide 5 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)(-2) + (3)(-1) = 1

Table of Contents Slide 6 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 7 Matrices - Multiplication Thus, the product of the matrices is...

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

Table of Contents Matrices - Multiplication