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

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Advance Math

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 Sspans Rn.
(c) Showthatdim(W)+dim(W⊥)=n.

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