Question: Prove that if 2 points violate an inequality, so does any point in their convex hull. In other words, given two points x1, x2 Rn,

Prove that if 2 points violate an inequality, so does any point in their convex hull. In other words, given two points x1, x2 Rn, and an inequality aT x b, prove that if aT x1 > b and aT x2 > b then aT x > b for all points x in the convex hull of x1 and x2

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