194 Chap 4 Duality Theory Exercise 426 Let A Be A

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194 Chap. 4 Duality theory Exercise 4.26 Let A be a given matrix. Show that exactly one of the fo…

Problem 4.26

194 Chap. 4 Duality theory Exercise 4.26 Let A be a given matrix. Show that exactly one of the following alternatives must hold. (a) There exists some x 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 state- ments are equivalent. (a) Every vector such that Ax > 0 and x > 0 rnust satisfy x1 = 0. (b) There exists some p such that p'A 0, p 0, and p'A1

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