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 W1 = 2v1 + V2 303 + 22 + 23 W1 = -21 - 203 2 u1 + 22 and 2 2 = V1 - 202 W2 = W3 = 3v1 + 303 W3 -2u1 - 23 (i) [3 marks] Find [wi]s and [wi]r for i = 1, 2,3 without using transition matrix. (ii) [3 marks] Use (i) to find the transition matrix from S to T. (iii) [2 marks] Use (ii) to find [vi]s for i = 1, 2, 3. (iv) [3 marks] Define the n x 3 matrices A = (u] U2 U3) and B = (v1 v2 V3). Find a matrix C such that A = BC. (Hint: Consider the augmented matrix (B | A).) - 2 -1 OT CO (v) [3 marks] Let A be as in (iv) such that A'A = Find wi . wj, for i, j = 1, 2, 3