For each n, define two linear maps and X: Pn(R) Pn+1(R), (Xp)(x)= = xp(x), pe P (R), x R (Dp)(x) = p'(x), pe P (R), z R. D: Pn(R) Pn-1 (R), For n 1 compute the composition Do X: P (R) P (R) and then: a) Compute the kernel of DoX b) Compute the image of Do X c) Determine if Do X is invertible d) Find the matrix of Do X with respect to the standard basis of P (R), using the isomorphism P (R) coming from the coordinate map e) What are the eigenvalues and eigenvectors of Do X? R"+1