Recent content by FightingWizard

Homework Statement Let S denote (x,y,z) in R3 which satisfies the following inequalities: -2x+y+z <= 4 x-2y+z <= 1 2x+2y-z <= 5 x >=1 y >=2 z >= 3 Homework Equations How to find the dimension of the set S ? The Attempt at a Solution I have tried to transform the inequalities into matrix form...

How do I then find the vector with the maximum length in the polyhedron?

Homework Statement Let P be the set of (x,y,z)^t in R^3, which satisfies the following inequalities: -2x+y+z <=4 x-2y+z<=1 2x+2y-z<=5 x>=1 y>=2 z>=3 Homework Equations I want to find the vector in the set with the maximal length. The Attempt at a Solution I have transformed the linear...

So I need to find the convex combination of the five given points and then check if the vector p lies in the convex hull of T, and if it does then I can use the definition of closure to see if it is closed. Is that correct?

Yes, the convex hull of a subset is the set of all convex linear combinations of elements from T, such that the coefficients sum to 1. But I don't understand how to use this to show that the subset T is closed and convex.

I don't understand "writing a completely general formula for an element of T". Can you explain what you mean by that?

We have a vector p = (0, 0, 2) in R^3 and we have the subset S = {xp where x >= 0} + T, where T is the convex hull of 5 vectors: (2,2,2), (4,2,2), (2,4,2), (4,4,6) and (2,2,10). How do I show that the subset T is a closed and convex subset? I know that a subset is called convex if it contains...