Let W be a subspace of Rn with an orthogonal basis {w1, w2, ..., wp} and...

Let W be a subspace of Rn with an orthogonal basis {w1, w2, ..., wp} and let {v1,v2,...,vq} be an orthogonal basis for W⊥. Let

S = {w1, w2, ..., wp, v1, v2, ..., vq}.

(a) Explain why S is an orthogonal set. (b) Explain why S spans Rn.

(c) Showthatdim(W)+dim(W⊥)=n.

Expert Solution

Colby Messinger answered 1 year ago

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