Let V = {p(t) ∈ $P_3$ | p(2) = 0}. V has bases B = {$t-2$, $(t-2)^2$, $(t-2)^3$} and C = {$t-2$, $t^2-2t$, $t^3-2t^2$}. Find the change of coordinates matrices from B to C and from C to B.
The only thing that is throwing me off is the p(2)=0 part. I don't know how to account for that constraint.
Hint: Express elements of $B$ in terms of elements of $C$ and vice-versa. The coefficients will give you the change of coordinates matrices.