Consider the (ordered) bases B = {1, 1+t, 1+2t+t2} and C = {1, t, t2} for P₂. Find the change of coordinates matrix from C to B. (a) (b) Find the coordinate vector of p(t) = t² relative to B. (c) The mapping T: P2 P2, T(p(t)) = (1+t)p' (t) is a linear transformation, where p'(t) is the derivative of p'(t). Find the C-matrix of T.
