# Does it make sense to examine the dual of a feasbility problem?

Consider a standard feasibility problem. The goal is to examine the state of feasible solutions for $Ax=b$ to find an $x$ that satisfies some property. Does the dual of this problem tell us anything about the solution? Since there is no objective function that we're examining I think the dual looks like $A^Tx \leq 0$. Is this right?

• An equality can be replaced by an inequality and a suitable objective function to form a primal. Currently you took a zero function for your primal, which does not work. – Parham Nov 16 '13 at 0:59
• The dual solution tells you something about the primal solution through complementary slackness. – Yuval Filmus Nov 16 '13 at 19:04