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Unformatted text preview: Math 136 Assignment 4 Solutions 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) 3 1 1 2 1 1 1 3 7 3 2 1 5 Solution: 3 1 1 2 1 1 1 3 7 3 2 1 5 = 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 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 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 4 3 1 1 2 1 1 4 6 = 3 12 3 11 (b) A = 1 3 1 2 1 4 1 3 , B = 6 2 2 1 1 3 2 3 4 . Solution: Since A and B are the same size, A + B is defined. Since the number of columns of A equals the number of rows of B , AB is defined. ( A + B ) T = 7 1 3 1 2 7 3 3 7 T = 7 1 3 1 2 3 3 7 7 A T + B T = 1 2 1 3 1 1 4 3 + 6 1 2 2 1 3 2 3 4 = 7 1 3 1 2 3 3 7 7 (...
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 Spring '08
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 Math, Linear Algebra, Algebra

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