{{{id=1|
x_1 +2x_2-4x_3-x_4 = 32
x_1 +3x_2 -7x_3 -x_5 = 33
x_1 +2x_3 -2x_4 +3x_5 = 22
///
}}}
{{{id=2|
A=matrix(QQ,[[1,2,-4,-1,0,32],[1,3,-7,0,-1,33],[1,0,2,-2,3,22]])
show(A)
///
\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrr}
1 & 2 & -4 & -1 & 0 & 32 \\
1 & 3 & -7 & 0 & -1 & 33 \\
1 & 0 & 2 & -2 & 3 & 22
\end{array}\right)
}}}
{{{id=3|
A.rescale_row(0,1)
show(A)
///
}}}
{{{id=4|
A.add_multiple_of_row(1,0,-1)
show(A)
///
\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrr}
1 & 2 & -4 & -1 & 0 & 32 \\
0 & 1 & -3 & 1 & -1 & 1 \\
1 & 0 & 2 & -2 & 3 & 22
\end{array}\right)
}}}
{{{id=5|
A.add_multiple_of_row(2,0,-1)
show(A)
///
\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrr}
1 & 2 & -4 & -1 & 0 & 32 \\
0 & 1 & -3 & 1 & -1 & 1 \\
0 & -2 & 6 & -1 & 3 & -10
\end{array}\right)
}}}
{{{id=6|
A.add_multiple_of_row(2,1,2)
show(A)
///
\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrr}
1 & 2 & -4 & -1 & 0 & 32 \\
0 & 1 & -3 & 1 & -1 & 1 \\
0 & 0 & 0 & 1 & 1 & -8
\end{array}\right)
}}}
{{{id=7|
A.add_multiple_of_row(0,1,-2)
show(A)
///
\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrr}
1 & 0 & 2 & -3 & 2 & 30 \\
0 & 1 & -3 & 1 & -1 & 1 \\
0 & 0 & 0 & 1 & 1 & -8
\end{array}\right)
}}}
{{{id=8|
A.add_multiple_of_row(1,2,-1)
show(A)
///
\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrr}
1 & 0 & 2 & -3 & 2 & 30 \\
0 & 1 & -3 & 0 & -2 & 9 \\
0 & 0 & 0 & 1 & 1 & -8
\end{array}\right)
}}}
{{{id=9|
A.add_multiple_of_row(0,2,3)
show(A)
///
\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrr}
1 & 0 & 2 & 0 & 5 & 6 \\
0 & 1 & -3 & 0 & -2 & 9 \\
0 & 0 & 0 & 1 & 1 & -8
\end{array}\right)
}}}
{{{id=10|
///
}}}