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**yago.dorea****Member**- Registered: 2012-09-09
- Posts: 6

Hello, I want to prove that the determinant of Fibonacci's nxn tridiagonal matrix is equal to the (n+1)th term of the Fibonacci sequence.

I'm trying to do it by induction, stating that **det(F(n)) = det(F(n-1)) + det(F(n-2))** (yeah I don't know how to use LaTex)

but I don't know how to prove that the minor M(n, n-1)(F(n)) = det(F(n-2))

Thanks.

Live long and prosper.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,358

Hi;

Try this pdf ( first page ) and see if any of it helps.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**yago.dorea****Member**- Registered: 2012-09-09
- Posts: 6

Ah I got it, you start from the beggining, I was doing the cofactors of the last terms... Thank you!

Live long and prosper.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,358

Hi yago.dorea;

Your welcome and welcome to the forum.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**yago.dorea****Member**- Registered: 2012-09-09
- Posts: 6

I'm glad I found this forum. I am being amazed by some topics in the "Dark Discussions at Cafe Infinity" section. Mainly one article about the Vandermonde Determinant.

Live long and prosper.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,358

Hi yago.dorea;

Yes, there is good stuff here.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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