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Unformatted text preview: with reasoning based on theorems, deﬁnitions, or counterexamples. a) If ~v 1 is a vector in R n , then the set { ~v 1 } is linearly independent. b) If { ~v 1 ,...,~v k } is a linearly dependent set in R n , then { ~v 1 ,...,~v k1 } is linearly dependent. c) If { ~v 1 ,~v 2 } is a linearly independent set in R n , then { ~v 1 ,~v 1~v 2 } is linearly independent. * 5. Let ~x = ± a b ² , ~ y = ± c d ² , and ~ z = ± e f ² be any three vectors in R 2 . a) Prove that { ~x,~ y } is linearly independent if and only if adbc 6 = 0. b) Prove that { ~x,~ y,~ z } is linearly dependent. * Indicates a challenging problem....
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 Spring '08
 All
 Linear Algebra, Algebra, Vectors, Sets

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