Ax=b proof

[BobSea]

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.

[jbunniii]

Your reasoning is correct. For a counterexample, try a very simple A whose columns are elements of the standard basis for \mathbb{R}^m.