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Matrices - Multiplication

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

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  1. 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.

  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. Slide 2

  3. 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

  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 Slide 4

  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 Slide 5

  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 ... Slide 6

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

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

  9. Matrices - Multiplication END OF PRESENTATION Click to rerun the slideshow.

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