12.5 Consider the linear equality problem (LEP): minimize ExTr + cTx subject to Ax = b, where c = (1, 1, 1), A = [1 -1 1], b = 1. (a) Write down a null space basis Z for the matrix A. (b) Let xo = (1, 1, 1) be an initial point, Write down the projected Hessian ZGZ and projected gradient Z g at To. (c) Compute a search direction p using To as an initial starting point. (First find p, and then determine p = Zpz.) (d) Compute the next approximation (iterate) x1. (e) Show that x] is a minimizer