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I recently came across this question, and the way I think people usually go about this is to find a certificate that answers 'yes' to the decision problem 'Is this LP infeasible?' Or, given a certificate, verify if that yields infeasibility or not. I know of the theorem that says Ax = b is infeasible if there exists y such that ATy = 0 and yTb = 1. (AT = transpose of A). So given a y, we can check in polynomial time if these two conditions hold, and that is why the infeasibility problem is in NP. Am I missing something, or is this a good enough approach?

Namrata Banerji
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I expect you'll also have to prove that: (1) the "infeasible if" is an "infeasible iff", (2) the "size" of $y$ (the number of bits needed to represent it) is polynomial in the size of $A,b$, and (3) you can find $y$ in polynomial time.

D.W.
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