I am trying to solve a system of linear equations that is underdetermined. Meaning the number of unknown is more than the equations. The system is of the form $Ax=0$. I have seen methods of solving this type of problem when the right hand side is nonzero. Namely, $Ax=b\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}x=({A}^{T}A{)}^{-}{A}^{T}b$. But this method is inapplicable when $b=0$. Any suggestions?