5. S = {ul, u2, us} and T = {v1, v2, v3} be two ordered bases for a subspace W in R". Suppose w1, w2, w3 E W such that + 303 W1 = 2v1 + - = -41 + u2 + 43 203 W1 and = V1 - 202 = 2u1 + 2 3v1 + 3v3 W02 W3 = W03 -2u1 (i) Find [wi]s and [wi]r for i = 1,2,3 without using transition matrix. (ii) Use (i) to find the transition matrix from Sto T. (iii) Use (ii) to find [v;]s for i = 1, 2, 3. (iv) Define the nx3 matrices A = (ujugu;) and B = (v1 V2 V3). Find a matrix C such that A = BC. (Hint: Consider the augmented matrix (B | A).) &LN (v) Let A be as in (iv) such that AA = Find wi . wj, for i, j = 1, 2, 3