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MA353_HW1_sol

MA353_HW1_sol - 0 ± Proof of Corollary 2 of Theorem 11 Let...

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Purdue University MA 353: Linear Algebra II with Applications Homework 1, due Jan. 22, solutions Sec. 1.2 1 (c): False. Proof. Let’s choose x = 0 V . Then for any choice of a and b , clearly ax = bx , even when a 6 = b . 18: False. Proof. (VS 1) is not satisfied. For example, let ( a 1 , a 2 ) = (1 , 0) and ( b 1 , b 2 ) = (0 , 0). Then ( a 1 , a 2 ) + ( b 1 , b 2 ) = (1 , 0) but ( b 1 , b 2 ) + ( a 1 , a 2 ) = (2
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Unformatted text preview: 0). ± Proof of Corollary 2 of Theorem 11, Let x ∈ V . Suppose y and y are vectors in V such that x + y = 0 and x + y = 0. We need to show y = y . But x + y = 0 and x + y = 0 imply x + y = x + y , which implies y + x = y + x . Then by Theorem 1.1, we have y = y . ± 1...
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