(a) Define, A = 0 -1 3 7 0 1 4 - and c = (-1 1 -2 -1 5) The Linear Program, min{c'r : Ar = b, r > 0}, dua (P) is unbounded. Guess a certificate of unboundedness and PROVE that it indeed certifies that the Linear Program is unbounded. (b) Define, 2 3 1 4 3 = V 0 13 and b = 2 2 09 There is no solution to the system Ar = b,r 2 0. Guess a certificate of infeasibility y and PROVE that it indeed certifies that there is no solution. HINT: for all i, pick y c {0, +1, +2}- (c) Prove that the system of linear constraints Ar = b has no solution if there exists y such that ATy =0 and by / 0. The converse in fact holds, namely, if Ar = b has no solution then it is because there exists y with A y = 0 and b y / 0. In fact you have seen this result in your Linear Algebra class, but it was stated in a different language. Can you recognize the result? JUSTIFY YOUR