Exercise 4.26 Let A be a given matrix. Show that exactly one of the following alternatives must hold.
(a) There exists some x does not equal 0 such that Ax = 0, x > 0.
(b) There exists some p such that p'A> 0'.
Exercise 4.27 Let A be a given matrix. Show that the following two statements are equivalent.
(a) Every vector such that Ax > 0 and x > 0 must satisfy x1 = 0.
(b) There exists some p such that p'A <0, p > 0, and p'A1 >0, where A1 is the first column of A.
Please see the attached file for the completely formatted problems.
Linear Programming, Duality, Feasibility and Optimal Solutions are investigated. The solution is detailed and well presented.
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