3. Consider the linear map, TEL(P(3(F), F)) given by the formula Tp= [***p() dr. (a) Compute (with proof) a basis for nullT and rangeT. (b) Compute M(T) with respect to the monomial basis. (c) Let S E L(P3(F)) denote the change of basis operator which transforms vectors from the monomial basis to the basis, B := = {x 1, x+1, (x - 1)', (x + 1)3}. Compute M(S) and use it to compute M(T) with respect to B. Hint: You can (but are not required to) check your answer by computing M(T) with respect to B directly using calculus or Wolfram Alpha. 3. Consider the linear map, TEL(P(3(F), F)) given by the formula Tp= [***p() dr. (a) Compute (with proof) a basis for nullT and rangeT. (b) Compute M(T) with respect to the monomial basis. (c) Let S E L(P3(F)) denote the change of basis operator which transforms vectors from the monomial basis to the basis, B := = {x 1, x+1, (x - 1)', (x + 1)3}. Compute M(S) and use it to compute M(T) with respect to B. Hint: You can (but are not required to) check your answer by computing M(T) with respect to B directly using calculus or Wolfram Alpha