8. EXTRA CREDIT [5 points] Suppose a pair of vectors x-M x2 x,]T ECn and y [y? ?? yn]T ECn are such that y-Fx, where 1 24 2 ,2 and ? ;; exp(-12n) E C. Matrix F is a bijective operator, also known as the (finite) Discrete Fourier Transform, and it has the inverse 2 that yields x-Fly. Notice that a-k-?-k for all k-1, 2, hence, we can write F1(w) F(w1). , n (because ??-1): Show that F-1F = FF-1-1. Hint: You may find the following fact helpful. Since "-1, we have wn(k-) - 1, or equivalently, ?kn-1, where ?k-uti. This translates into the equation 1-0'-0, or equivalently, (1-%)(1+9k+92 +9kn_ 1-0