Let T: P2 P3 be the transformation that maps a polynomial p(f) into the polynomial (t

Question:

Let T: P2 → P3 be the transformation that maps a polyno¬mial p(f) into the polynomial (t + 3)p(f).
a. Find the image of p(f) = 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}.