Given a in R, consider the evaluation map Ea: Pn R defined in Example 3. (a)

Question:

Given a in R, consider the evaluation map Ea: Pn → R defined in Example 3.
(a) Show that Ea is a linear transformation satisfying the additional condition that Ea(xk) = [Ea(xk)] = holds for all k = 0, 1, 2,.... [Note: x° = 1.]
(b) If T: Pn → R is a linear transformation satisfying T(xk) = [T(x)k] for all k = 0, 1, 2,..., show that T = Ea for some a in R.