MATLAB exercises: Create a script for the following exercises: 1. Let -6 28 21 A = 4 -15-12 -8 a 25 For each value of a in the set {32, 31.9, 31.8, 32.1, 32.2} find the eigenvalues of A and create a graph of the characteristic polynomial p(t) = det(A - I) for -1≤t≤4. Plot all the graphs on one coordinate system. (Hint: Remember the 'hold on' command we have used) 2. Let Ak be the Hilbert matrix of size k, with k = 2,..., 10. Plot in semilogarithmic scale the minimum and maximum (commands min and max) eigenvalue of Ak as a function of k. (The y axis should be logarithmic)