=for timestamp
Mo Mär 20 17:16:54 CET 2006

=head2 Der Gauß-Algorithmus

=begin comment

#!/usr/bin/perl

use warnings;
use strict;

print "M<\\begin{array}{rrr|l}\n";
while(<>) {
  chomp;
  @_ = split;
  printf "{} %s & %s & %s & %s \\\\\n", @_;
}
print "\\end{array}>\n\n";

=end comment

M<\begin{array}{rrr|l}
{} 10 & 1 & -2 & 2 \\
{} 1 & 2 & 2 & 3 \\
{} 4 & 4 & 3 & 5 \\
\\
{} 1 & 2 & 2 & 3 \\
{} 10 & 1 & -2 & 2 \\
{} 4 & 4 & 3 & 5 \\
\\
{} 1 & 2 & 2 & 3 \\
{} 0 & -19 & -22 & -28 \\
{} 4 & 4 & 3 & 5 \\
\\
{} 1 & 2 & 2 & 3 \\
{} 0 & -19 & -22 & -28 \\
{} 0 & -4 & -5 & -7 \\
\\
{} 1 & 2 & 2 & 3 \\
{} 0 & -4 & -5 & -7 \\
{} 0 & -19 & -22 & -28 \\
\\
{} 1 & 2 & 2 & 3 \\
{} 0 & 1 & \frac{5}{4} & \frac{7}{4} \\
{} 0 & -19 & -22 & -28 \\
\\
{} 1 & 2 & 2 & 3 \\
{} 0 & 1 & \frac{5}{4} & \frac{7}{4} \\
{} 0 & 0 & \frac{7}{4} & \frac{21}{4} \\
\\
{} 1 & 2 & 2 & 3 \\
{} 0 & 1 & \frac{5}{4} & \frac{7}{4} \\
{} 0 & 0 & 1 & 3 \\
\end{array}>

M<x_1 = 3 - 2x_2 - 2x_3 = 1;>

M<x_2 = \frac{7}{4} - \frac{5}{4}x_3 = -2;>

M<x_3 = 3;>