2. Let S = {v1, 2, v3, va} be a basis for a vector space V. For parts (i) to (iii) below, give your examples of subspaces in terms of the vectors in S. (i) [3 marks] Find two subspaces U, and Uq of V such that dim U, =3, dim U2 = 2, dim U, nU, = 1. (ii) [3 marks] Find a subspace W of V such that dim W = 2 and W does not contain any vector in S. (iii) [3 marks] If X, and X, are two different subspaces of V such that dim X, = dim X2 =3, what are the possible dimensions of X1 0X2? Given examples of X, and X2 for each such possible dimension. (iv) [3 marks True or false: If T' is a proper subset of V that contains S, then I cannot be a subspace of V. Justify your