b_{n}
\end{pmatrix}</tex>

Pentru a rezolva sistemul vom transforma toate elementele de sub diagonala principală a matricei extinse în $0$.
 
<tex>
\begin{pmatrix}
a_{11} &  a_{12} & \ldots & a_{1n} & b_{1}\\
a_{21} &  a_{22} & \ldots & a_{2n} & b_{2}\\
a_{31} &  a_{32} & \ldots & a_{3n} & b_{3}\\
\vdots & \vdots  & \ddots & \vdots \\
a_{n1} &  a_{n2} & \ldots  & a_{nn} & b_{n}
\end{pmatrix}
 
\rightarrow
 
\begin{pmatrix}
a_{11} &  a_{12} & \ldots & a_{1n} & b_{1}\\
0      &  a'_{22} & \ldots & a'_{2n} & b'_{2}\\
0      &  0      & \ldots & a'_{3n} & b'_{3}\\
\vdots & \vdots  & \ddots & \vdots \\
0 &  0 & \ldots  & a'_{nn} & b'_{n}
\end{pmatrix}
</tex>

h2. Aplicaţii