[20 marks] Consider the real, even vector f = [fo, f1, ..., fN-1], in which f = R, and fn = N-n (analogous to an even function, in which f(x) = f(-x)). Given the Discrete Fourier Transform (DFT), N-1 Fk = fn exp XP (-2wink) for k N = 0,..., N-1, n=0 prove that the vector of Fourier coefficients, F = [Fo, F1,..., FN-1], is also a real, even vector. Be sure to justify your steps.