Let W is a subspace of C and {u,..., u} be an orthonormal basis of W. Let v be an arbitrary vector in C. (a) (3 points) Show that (v - projwv) u; = 0 for all i and explain why v-projwv is in W. (b) (3 points) Show that every vector v in V can be written as v = W+W2 where w is in W and w2 is in W. (c) (3 points) Prove that Wn W = ({0}. (d) (3 points) Prove that dim W + dim W = n. (e) (3 points) If S is a subset of C", prove that (S) Spans