12. The "Jibonacci" numbers are the average of the two previous numbers: gr42 = (gk+1 + qk) sothatgk+29k+19k+1(a) Find A(b) Find the eigenvalues and eigenvectors of A.(c) Find the limit as n →∞ of A".(d) If go = 0 and g1 = 1 show that the limit of the Jibonacci sequence is ?.%3D

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Answered: 12. The "Jibonacci" numbers are the…

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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12. The "Jibonacci" numbers are the average of the two previous numbers: gk+2 = (gk+1 + gk) so that Ik+2 gk+1 A gk+1 (a) Find A (b) Find the eigenvalues and eigenvectors of A. (c) Find the limit as n 0 of An. (d) If go = 0 and gi = 1 show that the limit of the Jibonacci sequence is .