Problem 8 Let P, be the space of polynomials of degree less than 4 with real coefficients. Define L : P1 - PA by L(p(x)) = 5r-p"(x) - (3 + 2)p"(x) + 7p(2) a) [5 pts] Find the matrix representing L with respect to the standard basis S = {1, x, 13, r} } of Pi. Explain how this can be used to prove directly that L is a linear transformation. b) [4 pts] Let S' = {(4 + 3x), (2-23), (1+5x -x?), (x + r )}. Show that S is a basis for PA. c) [4 pts] Compute the base transition matrix g Ts. d) [3 pts] Use a) and c) to compute g Ly, the matrix representative of L with respect to the basis S