How to use Farkas' lemma to create a system that must have a solution, given $Ax=0,x\ge0, c\cdot x>0$ does not have one?

Question

Suppose the system: $Ax=0,x \geq 0, $ and $c \cdot x > 0$ does not have a solution.

How can I apply Farkas' lemma to create a system that must have a solution? I'm not so sure how to proceed, since the system doesn't resemble the typical system in Farkas' lemma.

score 1 · Accepted Answer · answered Apr 11 '13 at 07:20

1

Add to your unknowns $x_1,\ldots,x_n$ a new one $x_{n+1}=c\cdot x$.

answered Apr 11 '13 at 07:20

Boris Novikov

17,470

How to use Farkas' lemma to create a system that must have a solution, given $Ax=0,x\ge0, c\cdot x>0$ does not have one?

1 Answers1