Follow the instructions for Exercises 14 using p(x) instead of x. p(x) = 3 + 2x, B

Question:

Follow the instructions for Exercises 1–4 using p(x) instead of x.

p(x) = 3 + 2x, B = {1 + x, 1 - x}, C = {2x, 3} in P₁

Instructions From Exercise 1

(a) Find the coordinate vectors [x]_B and [x]_B of x with respect to the bases B and C, respectively.
(b) Find the change-of-basis matrix P_C←_B from B to C.
(c) Use your answer to part (b) to compute and compare your answer with the one found in part (a).
(d) Find the change-of-basis matrix P_B←_Cfrom C to B.
(e) Use your answers to parts (c) and (d) to compute [x]_B, and compare your answer with the one found in part (a).