Let Pk denote the vector space of all polynomials with degree less than or equal to k. Define a linear transformation T : P4 ! P
3 by T(f(x)) = f(0)+f '1)(x-1)+f ''(2)(x-2)^2+f'''(3)(x-3)^3. Find the matrix representation for T relative to the standard basis {1; x; x^2; x^3; x^4} of R4 and the reversed standard basis {x^3; x^2; x; 1} of R3.
