4. Let V = span(S), where S = {(3,1,0,1,4), (3,4,1,3,6), (1,2, -1,0,2)}. (i) Prove that S...

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4. Let V = span(S), where S = {(3,1,0,–1,4), (3,4,1,3,6), (1,2, -1,0,2)}. (i) Prove that S is a basis for V. (ii) Prove that T is also a basis for V, where T = {(5,3,2,2,8), (7,8,5,9, 14), (4,3, –1,–1,6)}. (iii) Find the transition matrix from T to S. (iv) Find the transition matrix from S to T. (v) Suppose that (w)s = (3,–1,2). Find w and (w)T. 4. Let V = span(S), where S = {(3,1,0,–1,4), (3,4,1,3,6), (1,2, -1,0,2)}. (i) Prove that S is a basis for V. (ii) Prove that T is also a basis for V, where T = {(5,3,2,2,8), (7,8,5,9, 14), (4,3, –1,–1,6)}. (iii) Find the transition matrix from T to S. (iv) Find the transition matrix from S to T. (v) Suppose that (w)s = (3,–1,2). Find w and (w)T.