Matrices - Multiplication

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# Matrices - Multiplication - PowerPoint PPT Presentation

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 B m  n p  q. .

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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 B

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.

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.

Slide 2

2  4

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.

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

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)(-2) + (3)(-1) = 1

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 ...

Slide 6

Matrices - Multiplication

• Thus, the product of the matrices is ...

Slide 7

Matrices - Multiplication

• Example 2:
• Find CD where C and D are given by ...