Let S be a nonempty convex set in n with 0 S 1 For every point a S, define the polar set S a x n x 1 xTa yen 0 S a is a nonempty closed set 2 For any finite set of points a1, a2, , am in S, let A be the m Atilde n matrix whose rows are ai The system 72 ...

1 For every a let a be the polar set a x x 1 xa 0 a is nonempty since 0 a Let x be the limit o ...

Let S be a nonempty convex set in n with 0 S. 1. For every point a

Question:

Let S be a nonempty convex set in „œn with 0 ˆ‰ S.
1. For every point a ˆˆ S, define the polar set S*a = {x ˆˆ „œn : ||x|| = 1; xTa ‰¥ 0}. S*a is a nonempty closed set.
2. For any finite set of points {a1, a2, ..., am} in S, let A be the m Ã— n matrix whose rows are ai. The system