Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#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.

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,370

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#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.

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,370

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#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.

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,370

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

Board footer

Powered by FluxBB