Let be the matrix of T: P2 P2 with respect to the basis B = (v1, v2,

Question:

Let

be the matrix of T: P2 †’ P2 with respect to the basis B = (v1, v2, v3), where v1 = 3x + 3x2, v2 = -1 + 3x + 2x2, v3 = 3 + 7x + 2x2.
(a) Find [T(v1)]B, [T(v2)]B, and [T(v3)]B.
(b) Find T(v1), T(v2), and T(v3).
(c) Find a formula for T(a0 + a1x + a2x2).
(d) Use the formula obtained in (c) to compute T(1 + x2).