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 = 1- 1 2 3 1 5 2 2 3 . Solution: To determine if A is invertible we write [ A | I ] and row reduce: 1- 1 2 1 0 0 3 1 5 0 1 0 2 2 3 0 0 1 ∼ 1- 1 2 1 4- 1- 3 1 1- 1 1 Since the RREF of A will not be I , it follows that A is not invertible. b) B = 1- 1 0 2 1 1 0 2- 2 3 5 1 1 3 . Solution: To determine if E is invertible we write [ E | I ] and row reduce: 1- 1 0 2 1 0 0 0 1 1 0 0 1 0 0 2- 2 3 5 0 0 1 0 1 1 3 0 0 0 1 ∼ 1 0 0 0 10 3 8 3- 1 3- 5 3 0 1 0 0 1 3 2 3- 1 3 1 3 0 0 1 0- 1 3 1 3 1 3- 1 3 0 0 0 1- 1- 1 1 . Since the RREF of E is I , it follows that E is invertible and E- 1 = 10 3 8 3- 1 3- 5 3 1 3 2 3- 1 3 1 3- 1 3 1 3 1 3- 1 3- 1- 1 1 2. Let B = 2- 1 1 1 1 1- 1- 1 . Find B- 1 and use it to solve B~x = ~ d , where ~ d = (4 ,- 2 , 3). Solution: To find the inverse of B we write [ B | I ] and row reduce: 2- 1 1 1 0 0 1 1 0 1 0 1- 1- 1 0 0 1 ∼ 1 0 0 1 1 0 1 0- 1 / 2 3 / 2 1 0 0 1 1 / 2- 1 / 2- 1 Therefore B- 1 = 1 1- 1 / 2 3 / 2 1 1 / 2- 1 / 2- 1 . We have ~x = B- 1 ( B~x ) = B- 1 4- 2 3 = 1 1- 1 / 2 3 / 2 1 1 / 2- 1 / 2- 1 4- 2 3 = 1- 2 ....
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## This note was uploaded on 05/04/2010 for the course MATH 136 taught by Professor All during the Spring '08 term at Waterloo.

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

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