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## #1 2012-09-10 18:57:34

yago.dorea
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### 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.

## #2 2012-09-10 19:31:28

bobbym

Online

### 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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #3 2012-09-10 19:46:56

yago.dorea
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### Re: Fibonacci's determinant

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

## #4 2012-09-10 20:19:38

bobbym

Online

### 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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #5 2012-09-10 21:07:44

yago.dorea
Novice

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### 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.

## #6 2012-09-10 21:18:05

bobbym

Online

### 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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.