Fibonacci's determinant

yago.dorea · 2012-09-09 20:57:34

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.

bobbym · 2012-09-09 21:31:28

Hi;

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

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

yago.dorea · 2012-09-09 21:46:56

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

bobbym · 2012-09-09 22:19:38

Hi yago.dorea;

Your welcome and welcome to the forum.

yago.dorea · 2012-09-09 23:07:44

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.

bobbym · 2012-09-09 23:18:05

Hi yago.dorea;

Yes, there is good stuff here.

Math Is Fun Forum

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

Fibonacci's determinant

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

Re: Fibonacci's determinant

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

Re: Fibonacci's determinant

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

Re: Fibonacci's determinant

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

Re: Fibonacci's determinant

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

Re: Fibonacci's determinant

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