I am not sure how to solve this exercise:
Find all solutions of $\begin{align*}2x_1-3x_2-7x_3+5x_4+2x_5&=-2\\ x_1-2x_2-4x_3+3x_4+x_5&=-2\\ 2x_1\qquad-4x_3+2x_4+x_5&=3\\ x_1-5x_2-7x_3+6x_4+2x_5&=-7\;. \end{align*}$
my row-reduced echelon matrix is:
$\pmatrix{1&0&-2&1&0&1\\ 0&1&1&-1&0&2\\ 0&0&0&0&1&1\\ 0&0&0&0&0&0}$
I don't see my mistake right now, I think I did something wrong xD
Thank you very much!