$$ \begin{pmatrix} 0 & 1 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 0 \\ \end{pmatrix} * x = \begin{pmatrix} 0 \\ 0 \\ 0 \\ \end{pmatrix} $$
What's the next step? 1 or 2? And why?
$$ \begin{pmatrix} 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 1 & 0 \\ \end{pmatrix} * x = \begin{pmatrix} 0 \\ 0 \\ 0 \\ \end{pmatrix} $$
$$ \begin{pmatrix} 0 & 1 & 1 \\ 0 & 0 & 0 \\ 1 & 1 & 0 \\ \end{pmatrix} * x = \begin{pmatrix} 0 \\ 0 \\ 0 \\ \end{pmatrix} $$
What's the algorithm of choosing free variable? If I choose x2 as a free variable, I get the right answer x = (-1, 1, -1), but why x2, not x1?