Let f R2 R2 be the linear transformation defined by Let : B -2 4 x. 100-** f(x) = {(1, 1), (−2, −1)}, be two different bases for R². a. Find the matrix [f] 1/3 for f relative to the basis B. [f] = b. Find the matrix [f] for f relative to the basis C. [f] = 188 c. Find the change-of-basis matrix Sc→B such that [v] B = Sc→B[V]C. SC→B = d. Find the transition matrix SB→c such that [v]C = SB C[V]B. Reminder: SB+C = (SC¬B)¯¹. SB-C: e. On paper, check that Sß→c[f]ßSc¬ß = [ƒ]C. с = {{−1, −1), (3, 2)}, Let T P3 P3 be the linear transformation such that : T(2x²) = 2x² – 4x, T(0.5x + 3) = 3x² + 2x = 3x²+2x-2, T(2x² + 1) = -2x – 3. - Find T(1), T(x), T(x²), and T(ax² + bx + c), where a, b, and c are arbitrary real numbers.