Question: (6) Let TE C(P(R) ) be defined by T(p(x)) = 3p(x) - up'(x). Let U be the 7-cyclic subspace of P(R) generated by q(x) =

(6) Let TE C(P(R) ) be defined by T(p(x)) = 3p(x) - up'(x). Let U be the 7-cyclic subspace of P(R) generated by

such that 8 = {q, T(q), . ... T"-'(q)} is a basis

(6) Let TE C(P(R) ) be defined by T(p(x)) = 3p(x) - up'(x). Let U be the 7-cyclic subspace of P(R) generated by q(x) = r* + 2r. (i) (4 marks) Determine the integer n such that 8 = {q, T(q), . ... T"-'(q)} is a basis for U. (ii) (4 marks) Find the matrix representation [7], where 8 is the ordered basis in (i).

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