assign8_soln

assign8_soln - Math 136 Assignment 8 Solutions 1. For each...

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Unformatted text preview: Math 136 Assignment 8 Solutions 1. For each of the following matrices, find the inverse, or show that the matrix is not invertible. a) A = 2 1 4 4 Solution: We have A- 1 = 1 2(4)- 1(4) 4- 1- 4 2 = 1 4 4- 1- 4 2 . b) B = 1 5- 3 1 3 1- 1- 4 1 Solution: Row reducing [ B | I ] gives 1 5- 3 1 0 0 1 3 1 0 1 0- 1- 4 1 0 0 1 1 5- 3 1- 2 4- 1 1 3 / 2 1 / 2 1 Since the RREF of B is not I , B is not invertible. 2. Let A = 1 2 3 1 2 4 1- 1 0 and B = 1 2 3 6 2 2- 1 1 0 . a) Find det A and det B . Solution: We have det A = 1 2 3 1 2 4 1- 1 0 = 1 3 3 1 3 4 1 0 0 = 3 det B = 1 2 3 6 2 2- 1 1 0 = 3 2 3 8 2 2 0 1 0 = 18 b) Find det( AB ). Solution: det( AB ) = det A det B = 54 c) Find det( A + B ). Solution: det( A + B ) = 2 4 6 7 4 6 0 0 0 = 0 1 2 d) Find A- 1 . Solution: We have 1 2 3 1 0 0 1 2 4 0 1 0 1- 1 0 0 0 1 1 0 0 4 / 3- 1 2 / 3 0 1 0 4 / 3- 1- 1 / 3 0 0 1- 1 1 Thus A- 1 =...
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This note was uploaded on 07/13/2011 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

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assign8_soln - Math 136 Assignment 8 Solutions 1. For each...

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