Can someone help me to solve this question please :
Establish, by induction, that : $ \forall n \in \mathbb{N} \setminus \{ 0,1 \} \ \forall v_1 , \dots , v_n \in \mathbb{R}^n $ linearly independants :
$ \mathcal{B}_{C_n^2} = \{ (v_1 - v_2) , (v_1 - v_3) , \ \dots \ , (v_1 - v_n) , ( v_2 - v_3 ) , ( v_2 - v_4 ) , \ \dots \ , (v_2 - v_n) , \ \dots \ , ( v_{n-1} - v_n ) \} $
is a family of linearly dependent vectors of $ \mathbb{R}^n $.
Thanks in advance for your help.