# A linear programming question, no feasible solution question

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.

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