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How to find determinant of the matrix NxN? $$ \left| \begin{array}{ccccc} a^{n} & (a - 1)^{n} & \cdots & (a-n)^{n} \\ a^{n - 1} & (a - 1)^{n - 1} & \cdots & (a-n)^{n - 1} \\ \cdots & \cdots & \cdots & \cdots \\ a & a - 1 & \cdots & a-n\\ 1 & 1 & \cdots & 1 \end{array} \right| $$

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    $\begingroup$ That appears to be a $(n+1) \times (n+1)$ matrix... $\endgroup$ – aras Dec 20 '15 at 12:30
  • $\begingroup$ There is N = (n + 1) $\endgroup$ – user3513483 Dec 20 '15 at 12:44
  • $\begingroup$ Hint: look up the formula for determinants of Vandermonde matrices. $\endgroup$ – HSN Dec 20 '15 at 12:47
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Check the article for Vandermonde Matrix!

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    $\begingroup$ Good job you beat me to this answer by about four seconds. $\endgroup$ – Gregory Grant Dec 20 '15 at 12:34

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