> Let g(x)=3+x. Let T: P2(R) P2(R) and U: P2(R) R3 be the lincar transformations respectively defined by T(f(x)) = f(x)g(x)+2f(x) and U(a + bx + cx) = (a + b, c, a - b). Let and y be the standard ordered bases of P2(R) and R3, respectively. Show Transcribed Text c (a) Compute [U], [T], and [UT] directly. Then use Theorem 2.11 to verify your result. (b) Let h(x)=3 - 2x + x2. Compute [h(x)] and [U(h(x))]. Then use [U] from (a) and Theorem 2.14 to verify your result.