Here is my matrix. How do I find the determinant of this one? I'm really trying to solve it but I can't think of anything.
$$ \begin{pmatrix} 3 & 2& ...& 2\\ 2& 3& ...& 2\\ 2& 2& 3& ...\\ 2& 2& ...& 3 \end{pmatrix} $$
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1asked many times, see http://math.stackexchange.com/questions/375711/eigenvector-of-matrix-of-equal-numbers for example. Nevertheless, i suggest you calculate the $n$ by $n$ determinant for $n=1,2,3.$ Not hard – Will Jagy Jun 17 '14 at 18:30
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That's the first thing I would do but I thought it wouldn't work for any number. – user3601507 Jun 17 '14 at 18:33
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Please do $n=1,2,3$ anyway. Call it "hands-on experience." A few cases is not a proof, but it is more than you currently know, and the practice really will help. – Will Jagy Jun 17 '14 at 18:36
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Alright I will try it now, thank you. Should I do it for X in the place of 3 and Y in the place of 2 for a more general approach? – user3601507 Jun 17 '14 at 18:36
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I suggest $3,2$ first. – Will Jagy Jun 17 '14 at 18:38
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It's $2n+1$ right? – user3601507 Jun 17 '14 at 18:46
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Yes you are right. – pointer Jun 17 '14 at 18:48
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I feel stupid for not doing that sooner. – user3601507 Jun 17 '14 at 18:49
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You are not alone thinking so:) – pointer Jun 17 '14 at 18:50
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See here for a generalization: http://math.stackexchange.com/questions/86644/determinant-of-a-specially-structured-matrix?lq=1 – Martin Sleziak Jun 18 '14 at 11:32
