Consider the ordered bases B = {1, x, x^2} and C = {1, (x - 1), (x - 1)^2} for P_2. (a) Find the transition matrix from C to B. (b) Find the transition matrix from B to C. (c) Write p(x) = a + bx + cx^2 as a linear combination of the polynomials in C. Now consider the "variable substitution" map T: P2 → P2, defined by T(P(x)) = p(2x – 1). In other words, T: p(x) → p(2x – 1). (d) Show that T is a linear transformation. (e) Find the matrix representation [T]_B of T with respect to the ordered basis B, (f) Find the matrix representation [T]_c of T with respect to the ordered basis C directly, using the definition of [T]_c. (g) Find the matrix representation [T]_c of T again, using [T]_B and the change of basis formula. (h) What can you say about the eigenvectors and eigenvalues of T? Give a brief explanation.