optimization - How do i show that the set S = { x : Ax < b } does not contain any extreme points

Question

I worked out the following, but this actually proves the opposite. Where am I going wrong?

Let x be an extreme point, then we can write x= ay + (1-a)z, where y, z in S, and 1< a< 0. Then y< A^(-1)b, and z< A^(-1)b, then x is also < A^(-1)b I'm stuck here

Answer 1

等待大神答复