Consider a system $Ax=b$ in which $A$ is an $n\times m$ matrix and $n < m$. Also the $rank(A)=n-1$. It is worthy to be noted that entries of matrix $A$ are partly rational. I need to solve this system exactly to find a feasible solution or proving that the system is inconsistent.
- What is the running time of Gauss-Jordan method to solve this system?
- Does there exist any method better than Gauss-Jordan to decide consistency or inconsistency of this system?