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Unformatted text preview: + c k1 x k1 = . Hence, c 1 x 1 + + c k1 x k1 +0 x n = . Since c 1 , ,c k1 , 0 are not all zero, we conclude by denition that x 1 , , x k1 , x k are linearly dependent. It contradicts to the fact that x 1 , , x k1 , x k are linearly independent. Hence x 1 , , x k1 must be linearly independent. / 1...
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This note was uploaded on 04/01/2008 for the course MATH 309 taught by Professor Samiabdul during the Spring '08 term at Michigan State University.
 Spring '08
 samiabdul
 Linear Algebra, Algebra

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