Given A E RmX", b 6 Rm, consider the pair of polyhedra P:={xR\":Ax2b}, Q:= {(y,z)ER2\":AyAz2b, yZO, 220} (a) Assume that 5: is an extreme point of P. Show that (g, 2) is an extreme point of Q, where :1] :2 max{zTc, 0} and Z :2 max{:, 0} are the positive and negative parts of :2. (b) Assume that (37,2) is an extreme point of Q such that 3] + E > 0 entrywise. Show that either 33 : 0 or 21' = 0 for each i, and that g 2 is an extreme point of P