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Exercise 4. Let -= (i ¹) = A € R²X2 1) Prove that for each n EN A" where F, is the i-th term of the Fibonacci sequence (Fo= 0, F₁ = 1, F₁+1 = F₁ + Fi-1). 2) Find an invertible matrix P such that PAP-1 is diagonal. 3) Find the general formula for the n-th term Fn. F₁ Fn+1,

Exercise 4. Let -= (i ¹) = A € R²X2 1) Prove that for each n EN A" where F, is the i-th term of the Fibonacci sequence (Fo= 0, F₁ = 1, F₁+1 = F₁ + Fi-1). 2) Find an invertible matrix P such that PAP-1 is diagonal. 3) Find the general formula for the n-th term Fn. F₁ Fn+1,

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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Exercise 4. Let A = - (1¹) 1) Prove that for each n EN € R²X2 ** ()-(.). = where F; is the i-th term of the Fibonacci sequence (Fo= 0, F₁ = 1, F₁+1 = F₁ + Fi-1). 2) Find an invertible matrix P such that PAP-1 is diagonal. 3) Find the general formula for the n-th term Fn-
Transcribed Image Text:Exercise 4. Let A = - (1¹) 1) Prove that for each n EN € R²X2 ** ()-(.). = where F; is the i-th term of the Fibonacci sequence (Fo= 0, F₁ = 1, F₁+1 = F₁ + Fi-1). 2) Find an invertible matrix P such that PAP-1 is diagonal. 3) Find the general formula for the n-th term Fn-
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