Linear Algebra Proof of Span and orthogonal vector space

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Let w=span(w1, w2, ......,wk) where wi are vectors in R^n. Let dot product be inner product for R^n here. Prove that if v*wi=0 for all i-1,2,....,k then v is an element of w^upside down T (w orthogonal).
 
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Take an element x of W. You must prove that v.x=0.

Try to prove this by expressing x as a linear combination of the wj.
 

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