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assign5_practice_soln

# assign5_practice_soln - Math 136 Practice Problems 5 1...

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Math 136 Practice Problems # 5 1. Calculate the following products or explain why the product is not defined. (a) 1 2 - 1 2 3 1 - 4 1 5 6 3 - 1 Solution: Since the number of columns of the first matrix does not equal the number of rows of the second matrix, the product is not defined. (b) 0 3 - 1 - 1 2 - 1 1 1 3 7 - 3 2 - 1 5 0 Solution: 0 3 - 1 - 1 2 - 1 1 1 3 7 - 3 2 - 1 5 0 = 1 - 3 - 8 1 - 24 - 4 (c) 2 1 5 - 3 1 2 Solution: 2 1 5 - 3 1 2 = - 6 2 4 - 3 1 2 - 15 5 10 (d) - 3 1 2 2 1 5 Solution: - 3 1 2 2 1 5 = 5 1

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2 2. For the given matrices A and B , check whether A + B and AB are defined. If so, check that ( A + B ) T = A T + B T and ( AB ) T = B T A T . (a) A = 1 1 4 - 2 1 6 , B = 5 4 - 2 3 0 - 1 Solution: Since A and B are not the same size, A + B is not defined. Since the number of columns of A equals the number of rows of B , AB is defined. ( AB ) T = 3 3 - 12 - 11 T = 3 - 12 3 - 11 B T A T = 5 - 2 0 4 3 - 1 1 - 2 1 1 4 6 = 3 - 12 3 - 11 (b) A = 1 3 1 - 2 1 4 1 0 - 3 , B = 6 - 2 2 1 1 3 2 - 3 - 4 .
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assign5_practice_soln - Math 136 Practice Problems 5 1...

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