I have constructed augmented matrix

 

[math]

\left[ \begin{array}{ccccccc|c}

\frac{4}{5} & -1 & 0 & 0 & 0 & 0 & 0 & 1\\

0 & \frac{4}{5} & -1 & 0 & 0 & 0 & 0 & 1\\

0 & 0 & \frac{4}{5} & -1 & 0 & 0 & 0 & 1\\

0 & 0 & 0 & \frac{4}{5} & -1 & 0 & 0 & 1\\

0 & 0 & 0 & 0 & \frac{4}{5} & -1 & 0 & 1\\

0 & 0 & 0 & 0 & 0 & \frac{1}{5} & -1 & 0\\

\end{array}\right]

[/math]

 

and I would like to find all solutions.

 

How would I go about doing that?

No one familiar with underdetermined systems?

nope.

I don't really see the issue here. Use Gaussian elimination and then back substitution as per normal.

Hmm.. Just thought there were some way like with overdetermined systems.