7. (a) Suppose S = {u1, u2, ..., uk} is an orthogonal basis for a subspace V of Rn. Let S' = U1 U2 uk will'1221'' be an orthonormal basis of V obtained from normalizing S. If the coordinate vector of v with respect to S is given by (v)s = (C1 (2 ... Ck) , what is (v)s, the coordinate vector of v with respect to S'? (b) Let T = {u1, u2, ..., uk} be a basis for a subspace V C R" and T' = {W1, W2, ..., Wk} be an orthonormal basis of V obtained from T by applying the Gram-Schmidt process (Theorem 5.2.19) with normalisation so that each w; is a unit vector. Find the transition matrix P from T to T'. Give your answer in terms of U1, U2, ..., uk and w1, W2, ..., Wk