Hi

This may be basic, but i'd really appreciate some help.

The 3 augmented matrices are in reduced row echelon form. For each state *with a reason* the number of solutions

$\displaystyle \begin{pmatrix}1 &2 & 0 &1 \\0& 0 & 1 & 0 \\0& 0 & 0 & 1\\0& 0 & 0 &0\end{pmatrix}$

$\displaystyle \begin{pmatrix}1 & 2 & 0 &1 \\0 & 0 & 1 &2 \\0& 0 & 0&0\end{pmatrix}$

$\displaystyle \begin{pmatrix}1 & 0 & 0 &1 \\0 & 1& 0 &2 \\0& 0 & 1& 3\end{pmatrix}$