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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.

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Presentation on theme: "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."— Presentation transcript:

1 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.

2 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.

3 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

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) = 1 - 6 - 6 = -11

5 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

6 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...

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

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

9 Table of Contents Matrices - Multiplication

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