Hello I am currently trying to find the solution of a spring system without condition on border, so naturally my vector $b \in 0_{M\{n,1\}}$, I am resolving this system with an LU algorithm but obviously the solution belong to $0_{M\{n,1\}}$ too. Is there any algorithm solution other than $0$ ? Or do I have to modify my system to have $b $ not belonging to $0_{M\{n,1\}}$ ?
$A$ is a known square Matrix, $A \in M_{\{n,n\}}$, $X$ is the vector that I am looking for $X \in M_{\{n,1\}}$ and $b \in M_{\{n,1\}}$ with b = \begin{pmatrix} 0 \\ \vdots \\ 0 \end{pmatrix}
Thank You