0 1 For this problem and the next one do all your calculations in Z13. For your convenience, here is the multiplication table in Z13 and a bunch of multiples of 13: 2 3 4 5 6 7 8 9 10 11 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 10 11 12 2 0 2 4 6 8 10 12 1 3 5 7 9 11 3 0 3 6 9 12 2 5 8 11 1 4 7 10 40 4 8 12 3 7 11 2 6 10 1 5 9 5 0 5 10 2 7 12 4 9 1 6 1138 6 0 6 12 6 11 4 10 3 9 28 1 7 70 71 82 9 3 10 4 11 5 126 8 0 8 3 11 6 1 9 4 12 7 2 10 5 909 5 1 10 6 2 11 7 3 12 8 4 10 0 10 7 4 1 11 8 5 2 12 9 6 3 11 1197 5 3 1 12 10 8 6 4 2 0, 13, 39, 52, 65, 78, 91, 12 0 12 11 10 9 8 7 6 5 4 3 2 1 104, 117, 130, 143, 169 26, 156, Here is the Fourier matrix F4 for a = 8, working in Z13: 1 5 1 1 1 8 1 12 1 5 1 12 1 12 12 8 -5 Demonstrate how to multiply this matrix times c = by the fast Fourier method, using just two 2 products of 2 by 2 matrices times 2-vectors (do those products by hand/calculator, not by recursively doing the fast Fourier method). Show clearly what two 2 by 2 matrix products you perform and how you combine (adding vectors, multiplying rows of vectors by numbers) those products to get the desired answer. Since you can easily compute the product F4c by the usual approach, you will be penalized if your demonstration doesn't produce the correct