Prob 4. Let T: f(x) + (x - 1)² f'' (x) - 3(x - 1)f'(x) + f(x). Write down its matrix representation: (a) as a map in L(P3, P2) using the standard monomial bases both for the domain and codomain; (b) as a map in L(P3, P3) using the standard monomial basis both for the domain and codomain; (c) as a map in L(P3, P3) using the shifted monomial basis 1, x - 1, (x - 1)², (x - 1)³ for the domain and for the codomain.
Prob 4. Let T: f(x) = (x - 1)² f''(x) - 3(x - 1)f'(x) + f(x). Write down its matrix representation: (a) as a map in L(P3, P2) using the standard monomial bases both for the domain and codomain; (b) as a map in L(P3, P3) using the standard monomial basis both for the domain and codomain; (c) as a map in L(P3, P3) using the shifted monomial basis 1, x - 1, (x - 1)², (x - 1)³ for the domain and for the codomain.