2. (6 points total) Let N be a positive integer. There is a unique N x N matrix A such that for any length-N column vector v, the column vector Av is equal to the discrete Fourier transform of v. (The discrete Fourier transform is defined on the last slide of the FFT lecture.) In this question, we index the rows (resp., columns) of an N * N matrix from 0 to N - 1. (a) (3 points) Let s and t belong to {0,..., N - 1}. Give an expression for the row-s, column-t entry of A. (b) (3 points) Let k belong to {1,..., N 1}. Prove that the dot product of row k of A and column N k of A is equal to N. (Recall that the dot product of two vectors (uo, ... , UN-1) and (vo, ... , UN-1) is Eosi<>