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

p(x) = 1 + x², B = {1 + x + x², x + x², x²}, C = {1, x, x²} in P₂
 

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←_C from 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).