<div id="ccc"> Considrons les matrices de \( M_{4,n}(K) ) 
:
<center>\( 
A=
\begin{pmatrix}
 2   & a_{1,2} & a_{1,3} & \cdots & \cdots & a_{1,n} \\
 0   & 0      & 5      & a_{2,3} & \cdots & a_{2,n} \\
 0   & 0      & 0      & 7      & \cdots & a_{3,n} \\
 0   & 0      & 0      & 0      & \cdots & 0 \\      
\end{pmatrix}
	\qquad B=
\begin{pmatrix}
 1   & a_{1,2} & a_{1,3} & \cdots & \cdots & a_{1,n} \\
 0   & 0      & 0      & 0      & \cdots & 0 \\
 0   & 0      & 0      & \cdots & 0      & 3 \\
 0   & 2      & 0      & 0      & \cdots & 0 \\      
\end{pmatrix}
 \)</center>
	La matrice \( A ) est chelonne, la matrice \( B ) ne l'est pas.

\def{integer n=randint(5..8)}
\def{integer m=randint(4..7)} 
\def{integer r=randint(floor(min(\n,\m)/2)..min(\n,\m))}
\def{text liste=shuffle(\n)}
\def{text J=wims(sort items \liste[1..\r])}
\def{matrix A=pari(A=matrix(\m,\n); J=[\J];
	for(i=1, \r, A[i,J[i]]=random\(3)+1;
	if( J[i]<\n,for(j=J[i]+1 ,\n, A[i,j]=random\(5)-2))); A)}

\def{text bsl=wims(nospace \ \ )}
\def{text special=wims(nospace \ special)}
\def{text Ac= }
\for{i=1 to \m}
{\for{j=1 to \n}
{\def{text Ac=\j=\J[\i] ? \Ac \special{color=red}\A[\i;\j]
\special {color=black}:\Ac \A[\i;\j]}
\if{ \j<\n}{
\def{text Ac=\Ac&}}
}
\def{text Ac=\i<\m?\Ac \bsl}}
\reload{<img src="gifs/doc/etoile.gif" alt="rechargez" width="20" height="20">}
Autre exemple de matrice chelonnne : 
<center>\(\begin{pmatrix}\Ac\end{pmatrix})</center>
</div>