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(5) Diagonalize F

(5) Diagonalize F

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Fibonacci Numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... Define the Fibonacci sequence {f} by a recurrence relation ( 2nd order linear difference equation): Fibonacci matrix: fn+2=fn+l+fn, n≥0, fo=0, f₁=1. F-3
Transcribed Image Text:Fibonacci Numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... Define the Fibonacci sequence {f} by a recurrence relation ( 2nd order linear difference equation): Fibonacci matrix: fn+2=fn+l+fn, n≥0, fo=0, f₁=1. F-3
(5) Diagonalize F Or better: Orthogonally diagonalize F: F = PDP¹, where P-¹ = pª Note: Express P and D in terms of . (6) Find a close formula of f, using the results of the diagonalization above. Must show all work! (7) Extra credit: Using the result from (5), find lim n→∞ fn+1 Must show all work! fn
Transcribed Image Text:(5) Diagonalize F Or better: Orthogonally diagonalize F: F = PDP¹, where P-¹ = pª Note: Express P and D in terms of . (6) Find a close formula of f, using the results of the diagonalization above. Must show all work! (7) Extra credit: Using the result from (5), find lim n→∞ fn+1 Must show all work! fn
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