4. ) In each case below either prove that the statement is True or disprove it by giving an example showing that it is False. (i) If B is a fixed 2 2 matrix, then the set U = {A|A M22, AB = 0} is a subspace of M22.

ii) If u, v, w are vectors in a vector space V , then span {u, v, w} = span {u + v, u + w, v + w}

(iii) The set {x,sin2 x, cos2 x} is independent in F[0, 2]

(iv) {1 + x, x + x 2 , x2 + x 3 , x3} is a basis of P3.