Problem(2-a) (5 points) Suppose that $T: P_4(t)\to P_3(t)$ is defined by $T(f(t)) = f'(t)$.\Given basis $B = \{1, t, t^2, t^3, t^4\}$ and basis $C = \{1, t, t^2, t^3\}$ for $P_4(t)$ and $P_3(t)$, respectively.\Find $[T]_B^C$.
Problem(2-b) (4 points) Given $f(t) = 1 - 2t + 3t^2 - 4t^3 \in P_3(t)$, find $[f(t)]_B=?$\find $[T(f(t))]_C=?$ \and verify that $[T(f(t))]_C = [T]_B^C[f(t)]_B$.