<div class="dem">
<center>\( {\rm det }(A_1,...,\special{color=red}A_j+A_{j+1}\special{color=black},\special{color=blue}A_j+A_{j+1}\special{color=black}, ..., A_n)=0)</center>
<p>
<div class="aide"> d'aprs <font color="brown">\((D2))</font>. </div>
 

<center>\( {\rm det }(A_1,...,\special{color=red}A_j+A_{j+1}\special{color=black},\special{color=blue}A_j+A_{j+1}\special{color=black}, ..., A_n))
=
\( {\rm det }(A_1,...,\special{color=red}A_j+A_{j+1}\special{color=black},\special{color=blue}A_j\special{color=black}, ..., A_n)
+
{\rm det }(A_1,...,\special{color=red}A_j+A_{j+1}\special{color=black},\special{color=blue}A_{j+1}\special{color=black}, ..., A_n)
)
=
\( {\rm det }(A_1,...,\special{color=red}A_j\special{color=black},\special{color=blue}A_j\special{color=black}, ..., A_n)
+ {\rm det }(A_1,...,\special{color=red}A_{j+1}\special{color=black},\special{color=blue}A_j\special{color=black}, ..., A_n))

+\(
{\rm det }(A_1,...,\special{color=red}A_j\special{color=black},\special{color=blue}A_{j+1}\special{color=black}, ..., A_n))
+\({\rm det }(A_1,...,\special{color=red}A_{j+1}\special{color=black},\special{color=blue}A_{j+1}\special{color=black}, ..., A_n))
</center>

<div class="aide"> d'aprs <font color="brown">\((D1))</font>, </div>

<center>=
\( {\rm det }(A_1,...,\special{color=red}A_{j+1}\special{color=black},\special{color=blue}A_j\special{color=black}, ..., A_n)+
{\rm det }(A_1,...,\special{color=red}A_j\special{color=black},\special{color=blue}A_{j+1}\special{color=black}, ..., A_n))
</center>
<div class="aide"> d'aprs <font color="brown">\((D2))</font>. </div>
Donc,
<center>
\( {\rm det }(A_1,...,\special{color=red}A_{j+1}\special{color=black},\special{color=blue}A_j\special{color=black}, ..., A_n)+
{\rm det }(A_1,...,\special{color=red}A_j\special{color=black},\special{color=blue}A_{j+1}\special{color=black}, ..., A_n) =0)</center>

</div>