Linear Algebra with Applications

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Math 20F - Linear Algebra - Winter 2003 Quiz # 3 1 2 — February 4 Answers 1. Let S = n‡ x y · R 2 : x 2 y o . Is S a subspace of R 2 ?. Prove your answer. Don’t be frightened by the word “Prove”. It means the same as “Justify” or “Show your evidence”. For this particular problem, showing a counter-example to a closure property is enough. ANSWER: We show that S is not closed under vector addition. For example, ( 1 1 ) and ( - 1 1 ) are in S . However 1 1 + - 1 1 = 0 2 / S. 2. Let v 1 = 1 2 3 and v 2 = 4 5 6 . Is { v 1 , v 2 } a spanning set for R 3 . If not, give an example of a x R which is not in span ( v 1 , v 2 ). ANSWER: We need to determine whether there is a vector ( a b c ) T so
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