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Matrices - Multiplication PowerPoint PPT Presentation


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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 . AB m  n p  q. .

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Matrices - Multiplication

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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 ...

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.


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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.

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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.

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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

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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

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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 ...

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Matrices - Multiplication

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

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Matrices - Multiplication

  • Example 2:

  • Find CD where C and D are given by ...

  • The answer is ...

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Matrices - Multiplication

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