<div class="dem">
<center>\( 
{\rm det }(A_1,...,\special{color=red}B\special{color=black},..., ..., A_n
)
)
= 
\( 
{\rm det }(A_1,...,\special{color=blue}a_1A_1
+...+\special{color=red}a_mA_m\special{color=blue}+
 ...+a_nA_n\special{color=black},..., A_n
))

=
\(
{\rm det }(A_1,...,\special{color=blue}a_1A_1\special{color=black} ,..., A_n
))
+...+
\(
{\rm det }(A_1,...,\special{color=red}a_mA_m\special{color=black} ,..., A_n
))

+...+
\(
{\rm det }(A_1,...,\special{color=blue}a_nA_n\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_mA_m\special{color=black} ,..., A_n
))
</center>
<div class="aide"> d'aprs <font color="brown">\((D2))</font></div>
<center>
= \(\special{color=red}a_m\special{color=black} 
{\rm det }(A_1,...,\special{color=red}A_m\special{color=black} ,..., A_n
))

</center>

</div>