Question: Not sure how to start. (a) Define, 1 0 -1 7 A = 3 01 - -2 4 -1 b : and c = (-1

Not sure how to start.

(a) Define, 1 0 -1 7 A = 3 01 - -2 4 -1 b : and c = (-1 1 -2 -1 5) The Linear Program, min {c'x : Ax = b, x 2 0}, du (P) is unbounded. Guess a certificate of unboundedness and PROVE that it indeed certifies that the Linear Program is unbounded. 1 (b) Define, 2 3 1 4 A = 0131 and b = 2 2 1 There is no solution to the system Ax = b, x 2 0. Guess a certificate of infeasibility y and PROVE that it indeed certifies that there is no solution. HINT: for all i, pick yi E {0, +1, 12}. (c) Prove that the system of linear constraints Ax = b has no solution if there exists y such that Ay = 0 and b y # 0. The converse in fact holds, namely, if Ax = b has no solution then it is because there exists y with ATy = 0 and by * 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

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