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 deﬁnition 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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 Spring '08
 samiabdul
 Linear Algebra, Algebra, X1, xk

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