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Gaussian elimination

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Gauss Elimination

We consider the system of linear equations  Ax = b or

 
\left[ 
\begin{matrix}
   {a_{11} } & {a_{12} } & {...} & {a_{1n} }  \\ 
   {a_{21} } & {a_{22} } & . & {a_{21} }  \\ 
   . & . & . & .  \\ 
   {a_{n1} } & {a_{n1} } & . & {a_{nn} }  \\ 
\end{matrix}
\right]
\left[ 
\begin{matrix}
   {x_1 }  \\ 
   {x_2 }  \\ 
   .  \\
   {x_n }  \\
\end{matrix}
\right]
=
\left[ 
\begin{matrix}
   {b_1 }  \\ 
   {b_2 }  \\ 
   .  \\
   {b_n }  \\
\end{matrix}
\right]
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