Let T: P2 P4 be the transformation that maps a polynomial p(t) into the polynomial p(t)

Question:

Let T: P2 → P4 be the transformation that maps a polyno¬mial p(t) into the polynomial p(t) C 2t2p(t).
a. Find the image of p(t) = 3 - 2t C t2.
b. Show that T is a linear transformation.
c. Find the matrix for T relative to the bases {1, t, t2} and {1, t, t2, t3, t4}.