Please solve the following problem

4. Let T: EUR} ) P4011) be a linear transfonnation dened by T(p(tc)) = 3211' (1 :c) + p" (:5) where p' denotes the derivative of p. (i) Find the transfonnation matrix [T] of T with respect to the standard bases of P301?!) and 174(k). (ii) The polynomial q 6 P301!) has component vector (2, 8, 4, 1)T with respect to the non-standard basis {Lane + 32,2: 2:3} of P3012). Find q(:i:) and write down the component vector of q with respect to the standard basis of PEAR). (iii) Use [T] and part (ii) to nd T(q(m)). (iv) Find T(q(:r:)) directly