2. Consider the Fibonacci-like numbers given by Go = 0, G1 =1 and Gr+2 = 2G,+Gr+1• (a) Write down the first 10 numbers in the sequence. %3D %3D [Gr+1 G, A (b) Write down a matrix equation for the numbers of the form [Gr+2] Gr+1 (c) Find the eigenvalues of the resulting matrix A. (d) Hence find a formula for Gr+2 in terms of r, following the method in the lectures using the diagonalization of A.
2. Consider the Fibonacci-like numbers given by Go = 0, G1 =1 and Gr+2 = 2G,+Gr+1• (a) Write down the first 10 numbers in the sequence. %3D %3D [Gr+1 G, A (b) Write down a matrix equation for the numbers of the form [Gr+2] Gr+1 (c) Find the eigenvalues of the resulting matrix A. (d) Hence find a formula for Gr+2 in terms of r, following the method in the lectures using the diagonalization of A.
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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(d) please
Transcribed Image Text:2. Consider the Fibonacci-like numbers given by Go = 0, G1 = 1 and Gr+2 = 2G,+Gr+1.
(a) Write down the first 10 numbers in the sequence.
Gr+1
G,
A
(b) Write down a matrix equation for the numbers of the form
Gr+2
Gr+1
(c) Find the eigenvalues of the resulting matrix A.
(d) Hence find a formula for Gr+2 in terms of r, following the method in the lectures
using the diagonalization of A.
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