5. S = {ul, u2, u3} and T = {v1, v2, v3} be two ordered bases for a subspace W in R". Suppose w1, w2, w3 E W such that U2 + 303 W1 = 201 + = -U1 + U2 + u3 = V1 - 202 - 203 W1 and W2 241 + U2 + 303 W2 = W3 = 301 -2u1 U3 W3 = (i) Find [wi]s and [wi] 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 [vi]sfor i = 1, 2, 3. (iv) Define the nx3 matrices A = (uj uzu3) and B = (v1 V2 v3). Find a matrix C such that A = BC. (Hint: Consider the augmented matrix (B | A).) -1 (v) Let A be as in (iv) such that A A = Find w; . wj, for i, j = 1, 2, 3