$\displaystyle \begin{pmatrix}

1 & 1& \lambda &| 1\\

0& \lambda -1 &1-\lambda &| 0\\

0&1 &1-\lambda &|1-\lambda ^2

\end{pmatrix}$

cant we say that for lambda=1 we have endless solutions?

but also we can divide equation 2 and 3 by lambda-1 and after that so for lambda=1 we get that there is no solutions

so what is the correct solution