Question

Pn denotes the vector space of polynomials of degree n or less. The map
f : P3 -> P4 is given by f(p(x)) = xp(x) for all polynomials p(x) element of P3.
(i) Show that f is a linear map.
(ii) With respect to the bases {1, x, x2, x3} for P3 and {1, x, x2, x3, x4} for P4, write
down the matrix for f.