# Intersection of hyperplanes

A very basic question but i couldn't find another post about it:

Given $p$ non parallel hyper-plane in $\mathbb{R}^p$:

$\left(\begin{array}{cccc} c_{11} & a_{11} & .... & a_{1p} \\ ... & ... & ... & .... \\ c_{p1} & a_{p1} & .... & a_{pp} \end{array} \right)$

$||a_{i.}||=1$

What is the best (from a numerical standpoint of view) way to get the $p$ vector of coordinates $x$ of their intersection?

If the matrix A is non-singular, the intersection of the hyperplanes is simply the the solution of the linear system of equations $Ax=b$, where
$A= \left(\begin{array}{cccc} a_{11} & .... & a_{1p} \\ ... & ... & .... \\ a_{p1} & .... & a_{pp} \end{array} \right)$
$b= -\left(\begin{array}{cccc} c_{11} \\ ... \\ c_{p1} \end{array} \right)$