assign8_practice_soln

assign8_practice_soln - Math 136 Practice Problems # 8 1....

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Unformatted text preview: Math 136 Practice Problems # 8 1. For each of the following matrices, find the inverse, or show that the matrix is not invertible. a) A = 1 2 1- 2 4 3 4 4 Solution: To determine if A is invertible we write [ A | I ] and row reduce: 1 2 1 1 0 0- 2 4 0 1 0 3 4 4 0 0 1 ∼ 1 0 0- 4- 2 / 3 5 / 3 0 1 0 2 1 / 6- 2 / 3 0 0 1 1 1 / 3- 1 / 3 Hence, A- 1 = - 4- 2 / 3 5 / 3 2 1 / 6- 2 / 3 1 1 / 3- 1 / 3 . b) B = 4- 1- 1 2 3- 3 2 3 Solution: To determine if B is invertible we write [ B | I ] and row reduce: 4- 1- 1 1 0 0 2 3 0 1 0- 3 2 3 0 0 1 ∼ 1 0 0 1 / 3- 1 / 3 0 1 0- 3 3- 4 0 0 1 2- 5 / 3 8 / 3 Hence, B- 1 = 1 / 3- 1 / 3- 3 3- 4 2- 5 / 3 8 / 3 . c) C = - 1- 1 2 1- 1- 2 4- 3- 1 5 2- 1- 2 4 4 Solution: To determine if C is invertible we write [ C | I ] and row reduce: - 1- 1 2 1 0 0 0 1- 1- 2 4 0 1 0 0- 3- 1 5 2 0 0 1 0- 1- 2 4 4 0 0 1 ∼ - 1- 1 2 1- 1- 3 6 1 1 11- 10- 4- 1 1 1- 1- 1 1 Since the RREF of C will not be I , it follows that C is not invertible. 1 2 2. Let B = 1- 2 2- 1 1 3- 2- 3 . Find B- 1 and use it to solve B~x = ~ d , where ~ d = 1- 2 3 . Solution: To find the inverse of B we write [ B | I ] and row reduce: 1- 2 2 1 0 0- 1 1 0 1 0 3- 2- 3 0 0 1 ∼ 1 0 0- 3- 10- 2 0 1 0- 3- 9- 2 0 0 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_practice_soln - Math 136 Practice Problems # 8 1....

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