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## #1 2012-09-09 20:57:34

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

### Fibonacci's determinant

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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## #2 2012-09-09 21:31:28

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Fibonacci's determinant

Hi;

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

http://ocw.mit.edu/courses/mathematics/ … 0_soln.pdf

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #3 2012-09-09 21:46:56

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

### Re: Fibonacci's determinant

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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## #4 2012-09-09 22:19:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Fibonacci's determinant

Hi yago.dorea;

Your welcome and welcome to the forum.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #5 2012-09-09 23:07:44

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

### Re: Fibonacci's determinant

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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## #6 2012-09-09 23:18:05

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Fibonacci's determinant

Hi yago.dorea;

Yes, there is good stuff here.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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