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Prove the following is a convex set?

  1. Oct 21, 2012 #1
    1. The problem statement, all variables and given/known data
    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


    2. Relevant equations




    3. 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.
     
  2. jcsd
  3. Oct 21, 2012 #2

    LCKurtz

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    Are arbitrary what? What does it mean for ##x\in R^n## to satisfy ##x > 0##?
     
  4. Oct 21, 2012 #3
    A and b are any arbitrary number in R.
    All vectors in x E Rn are non-negative
     
  5. Oct 21, 2012 #4

    LCKurtz

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    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.
     
  6. Oct 21, 2012 #5
    I'm so sorry. b is a vector too. I don't understand this topic too well.
     
  7. Oct 21, 2012 #6

    LCKurtz

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