1
Soit \(A=\left( a_{i,j}\right) _{(i,j)\in \{1,...,n\}^{2}}\in M_{n}({\Rr})\) telle que : \[\begin{aligned} \forall i &\in &\{1,...,n\},\sum_{j=1}^{n}a_{i,j}\leq 1, \\ \forall (i,j) &\in &\{1,...,n\}^{2},a_{i,j}\in [0,1[.\end{aligned}\] Montrer que \(\left| \det(A)\right| <1.\)