In Exercises 1-3, find the matrix [T]C←B of the linear transformation T: V → W with respect to the bases 13 and C of V and W, respectively. Verify Theorem 6.26 for the vector v by computing T(v) directly and using the theorem.
1. T: P1 → P1 defined by T(a + bx) = b - ax,
B = C = {1, x}, v = p(x) = 4 + 2x
2. T: P1 → P1 defined by T(a + bx) = b - ax,
B = {1 + x, 1 - x}, C = P{1, x} v = p(x) = 4 + 2x
3. T: P2 →P2 defined by T(p(x)) = p(x + 2),
B = {1, x, x2} C = {1, x + 2, (x + 2)2},
v = p(x) = a + bx + cx2