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Can you help me with this $n\times n$ determinant? Can't find what from what i have to substract.. Spent hours of trying...

\begin{vmatrix} 1&\cdots& 1& 1& 4\\ 1 &\cdots&1 & 9& 1 \\ 1 & \cdots &16& 1 &1\\ \vdots & \dots& \vdots&\vdots&\vdots\\ (n+1)^2 &\cdots& 1& 1& 1 \end{vmatrix}

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closed as off-topic by Namaste, Did, Isaac Browne, mathematics2x2life, rtybase Apr 29 '18 at 8:50

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    $\begingroup$ Here's a MathJax tutorial :) $\endgroup$ – Shaun Dec 11 '17 at 19:41
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    $\begingroup$ You should give an account of what you tried in "hours of trying" and what you discovered. It will help Readers respond in a helpful way, and in the future make your question a more valuable post. $\endgroup$ – hardmath Dec 11 '17 at 20:11
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We can rewrite this matrix as $$ \pmatrix{0& \cdots & 0 & 0 & 2^2 - 1\\ 0 & \cdots & 0 & 3^2 - 1 & 0\\ 0 & \cdots & 4^2 - 1 & 0 & 0\\ \vdots & \ddots & \vdots & \vdots & \vdots\\ (n+1)^2 - 1 & \cdots & 0 & 0 & 0} + xx^T $$ where $x = (1,1,\dots,1)^T$. From there, it suffices to apply the matrix determinant lemma.

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  • $\begingroup$ Thank you for helping me! $\endgroup$ – Deividito Dec 11 '17 at 20:25

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