Q6. Consider the linear map D : Pn - Pn-1 given by: d D(p) = da p(x)] = p'(x) (a) (2 points) Write a matrix for D : P3 - P2 with the following bases: P3 = span {1, x, x2, x } P2 = span {1, x, x2]. (b) (4 points) Compute the rank of D : Pn Pn-1. (c) (4 points) Prove that D is surjective. Q7. (a) (8 points) Suppose that U and W are finite dimensional subspace of V. Prove that dim(U O W) = dim(U) + dim(W). (b) (2 points) Give an example of two subspaces U and W in R2 such that: dim (U + W)