Consider A, a given matrix. I want to show that exactly one of the following holds:
1) $\exists x\neq 0$ such that $Ax=0$
2) $\exists p$ such that $p^TA>0$
I tried proving that this is equivalent to Farkas' Lemma, but I couldn't really get anywhere. I also tried writing an LP problem and its dual to see if I get somewhere, but I don't know what to use as the vector in my objective function.