Be $n>1$ and $x_1,...,x_n \in \mathbb{R}$ show per Induction with $n \in \mathbb{N}$
$ V_n(x_1,...,x_n) := det\begin{pmatrix} 1 & x_1 & x_1^2 & ... & x_1^{n-1} \\ 1 & x_2 & x_2^2 & ... & x_2^{n-1} \\ ... & ... & ... & ... & ... \\ 1 & x_n & x_n^2 & ... & x_n^{n-1} \end{pmatrix} = \prod \limits_{i>j}(x_i - x_j) $
so i haven't done induction with matrices before. My idea is to split them into smaller parts like det(AB)=det(A)det(B), but im missing some knowledge. Im here completely lost.
