Linear Algebra Proof of Span and orthogonal vector space

[sbj5533]

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).

 

[micromass]

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 w_j.