4. Implementing Gradient Descent. In this question you will implement gradient descent for an easy problem: convex quadratic functions. Consider the problem: min : f(ac) = where Q is a (strictly) positive definite matrix, i.e., it is symmetric and all its eigenvalues are strictly positive. (a) Compute the gradient: Vf (x). (b) Implement gradient descent using three stepsize choices: nt = 1/t, nt = 1/vt, and etat = n. (c) Randomly generate data (make sure that your matrix Q is symmetric and strictly posi- tive definite) and plot your results for the first two choices. For the third, find values of n for which gradient descent converges, and for which it diverges