Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Ax=b proof

  1. Oct 27, 2010 #1
    1. The problem statement, all variables and given/known data
    The system Ax=b, with Amxn, and m>n, always has a solution when A has full rank. If False, give a counter example, if True, say why.



    2. Relevant equations
    None


    3. The attempt at a solution
    I want to say False because b doesn't need to be in the range of A, so Ax=b wouldn't have a solution. However, I'm having trouble making a counter example (i.e. A = 3x2 matrix and b = 3x1 matrix) that proves the point.
     
  2. jcsd
  3. Oct 27, 2010 #2

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Your reasoning is correct. For a counterexample, try a very simple A whose columns are elements of the standard basis for [itex]\mathbb{R}^m[/itex].
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook