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I'm studying for a test and I came across this question: Let $a_1, a_2, . . . a_m \in \Bbb R^n$ such that $m > n+1$. Assume that for the set of m inequalities $a_i^t x ≤ b_i$ there is no feasible solution. Prove that there are $n + 1$ inequalities out of the $m$ which are not feasible.

Any advice?

Thanks

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  • $\begingroup$ $m>n+1$ or $m \geq n+1$ ? $\endgroup$ – Jean Marie Nov 18 '18 at 17:42
  • $\begingroup$ m $> n+1$ I'm also confused about why the strict inequality is required $\endgroup$ – John Doe Nov 19 '18 at 13:03

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