Let W C R" be a subspace and let W- C R" be its orthogonal complement. Let S = {u1,..., uk} be an orthogonal basis for W and S' The goal of these exercises is to give two different arguments for the fact that {V1,..., vi} be an othogonal basis for W. (*) dim W + dim W+ = n. 4. Show that SUS' is an orthogonal basis for R" and deduce (*).

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