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Assume $x_1, . . . , x_n$ are numbers. Show that $$det\begin{pmatrix} 1 & x_1 & ... & x_1^{n-1} \\ 1 & x_2 & ... & x_2^{n-1} \\ & & ...\\ 1 & x_n & ... & x_n^{n-1} \\ \end{pmatrix}=∏_{i<j}(x_j-x_i).$$

I am really not sure on how to show this, I thought using induction might be a good way, but I don't really know how to go about it.

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marked as duplicate by Dietrich Burde, Saucy O'Path, Community Apr 2 at 20:08

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