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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 cv0v, 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 "v0v". 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 cv0v, 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 "v0v". Try both!

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 51EQ
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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 cv0v, 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 "v0v". 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 cv0v, 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 "v0v". Try both!
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