Prove the following is a convex set?

[ashina14]

Homework Statement

Prove that F = {x E R^n : Ax >/= b; x >/= 0} is a convex
set.

Yes x in non negative and A and b are any arbitrary

Homework Equations

The Attempt at a Solution

Well I know A set T is convex if x1, x2 E T implies that px1+(1-p)x2 E T for all 0 <= p <= 1.
I don't know how to use this information.

 

[LCKurtz]

Homework Statement

Prove that F = {x E R^n : Ax >/= b; x >/= 0} is a convex
set.

Yes x in non negative and A and b are any arbitrary

Are arbitrary what? What does it mean for $x\in R^n$ to satisfy $x > 0$?

 

[ashina14]

A and b are any arbitrary number in R.
All vectors in x E Rn are non-negative

 

[LCKurtz]

Homework Statement

Prove that F = {x E R^n : Ax >/= b; x >/= 0} is a convex
set.

Are arbitrary what? What does it mean for $x\in R^n$ to satisfy $x > 0$?

A and b are any arbitrary number in R.
All vectors in x E Rn are non-negative

This doesn't make any sense to me. If x is a vector and A is a real number then Ax is a vector. If b is a real number you have the vector Ax > b, a real number. What does it mean for a vector to be greater than a number? It makes about as much sense to say an apple is greater than a bicycle.

 

[ashina14]

I'm so sorry. b is a vector too. I don't understand this topic too well.

 

[LCKurtz]

That doesn't help. What does it mean for one vector to be greater than another?