(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Ax=b proof

**Physics Forums | Science Articles, Homework Help, Discussion**