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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

    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


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    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].
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