Questions: ks 1. (a) Let B and C be two bases of R3 defined by: B = ( ( !) . ( 4 ).(:) Define a vector [ulg = (-3, 7, 8)". Find the matrix of change of bases [B]c and hence the vector in the new basis, [ulc. (b) Let T : Rm -> R". Define the image of T as S = {T(U) |UE Rm}. Show that S forms a subspace of Rn. Note: The aim of this problem is to prove a statement in the notes (Prop. 4.50). Citing this result does not constitute a proof.Proposition 4.50. Let T: U - V be a linear map between two vector spaces. The kernel of T is a subspace of U, and the image of T is a subspace of V