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Mastering a Weird Operation: Matrix Multiplication

Mastering a Weird Operation: Matrix Multiplication . Example #1. Use your calculators to find, if possible, AB and BA, where . Matrix Multiplication. If A is a matrix of order n X m and B is a matrix of order m X p, then AB is a matrix of order n X p. We find the rows of AB as follows:

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Mastering a Weird Operation: Matrix Multiplication

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  1. Mastering a Weird Operation: Matrix Multiplication

  2. Example #1 Use your calculators to find, if possible, AB and BA, where

  3. Matrix Multiplication • If A is a matrix of order n X m and B is a matrix of order m X p, then AB is a matrix of order n X p. We find the rows of AB as follows: • We multiply the first row of A by each column of B. This gives the first row of AB. • We multiply the second row of A by each column of B. This gives the second row of AB • We repeat this with all the rows of A.

  4. Explaining the answer to Example #1! • A has order 1 X 3 and B has order 3 X 2. • Since the number of columns of A is the same as the number of rows of B, • the product AB is defined and has order 1 X 2. • We compute AB by the procedure described earlier: • Multiply the row of A by the 1st column of B • Multiply the row of A by the 2nd column of B

  5. Example #2 Find AB if

  6. A has order 2 X 3 and B has order 3 X 2. • Since the number of columns of A is the same as the number of rows of B, • the product AB is defined and has order 2 X 2. • We compute AB by the procedure described earlier: • Multiply the 1st row of A by each column of B • Multiply the 2nd row of A by each column of B End of Example #2

  7. Example #3 • Which product is defined: AB or BA? • Compute the defined product.

  8. A has order 2 X 2 and B has order 4 X 2. • Since the number of columns of A is not the same as the number of rows of B, the product AB is not defined • Since the number of columns of B is the same as the number of rows of A, the product BA is defined • We compute BA by the procedure described earlier: • Multiply the 1st row of B by each column of A • Multiply the 2nd row of B by each column of A • Multiply the 3rd row of B by each column of A • Multiply the 4th row of B by each column of A

  9. Example #4 • Find x, y, and z if AB = C where

  10. Given AB = C, we have: • We first multiply the matrices on the left to obtain: • By equality of matrices, we have:

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