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Problem 2 (Completing the proof of Proposition 1) Let V be a vector space. Prove that the following two properties are true. 1. For every cЄR, we have c Oy = 0v. 2. If c.v = Oy, then either c = 0 or v = 0y. Hint: when tackling a proof like this, your proof should have two cases: first, you should assume that c = 0, in which case there is nothing else to do; next, you should assume that c 0, and use it to show that necessarily v = 0. Alternatively, your proof could be split into the cases "v=0y" and "v0y". Try both!

Problem 2 (Completing the proof of Proposition 1) Let V be a vector space. Prove that the following two properties are true. 1. For every cЄR, we have c Oy = 0v. 2. If c.v = Oy, then either c = 0 or v = 0y. Hint: when tackling a proof like this, your proof should have two cases: first, you should assume that c = 0, in which case there is nothing else to do; next, you should assume that c 0, and use it to show that necessarily v = 0. Alternatively, your proof could be split into the cases "v=0y" and "v0y". Try both!

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 2 (Completing the proof of Proposition 1) Let V be a vector space. Prove that the following two properties are true. 1. For every cЄR, we have c Oy = 0v. 2. If c.v = Oy, then either c = 0 or v = 0y. Hint: when tackling a proof like this, your proof should have two cases: first, you should assume that c = 0, in which case there is nothing else to do; next, you should assume that c 0, and use it to show that necessarily v = 0. Alternatively, your proof could be split into the cases "v=0y" and "v0y". Try both!
Transcribed Image Text:Problem 2 (Completing the proof of Proposition 1) Let V be a vector space. Prove that the following two properties are true. 1. For every cЄR, we have c Oy = 0v. 2. If c.v = Oy, then either c = 0 or v = 0y. Hint: when tackling a proof like this, your proof should have two cases: first, you should assume that c = 0, in which case there is nothing else to do; next, you should assume that c 0, and use it to show that necessarily v = 0. Alternatively, your proof could be split into the cases "v=0y" and "v0y". Try both!
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