] *CountAlg.java - Notepade Edit Format View HelpLn 28, Col 1100%Windows (CRLF)UTF-8Problem 2. The Fibonacci numbers are defined byFo = 0, F1 = 1, F = Fr + Fx-1 for k = 1, 2, ....Relations such as this are called recurrence relations or difference equations. We can recast this relation in "initial-value problem" form as follows:() - ( :) (A).(E) - ()Fk+11Fkk = 1, 2, ...k-1It is apparent from this that(2)-G )" (E).k-1F1(A).Fkk = 2,3, ....Find F30 as follows: First find the eigenvalues and associated eigenvectors of A := (}); next, find P, P-1, and Dthat satisfy A = PDP-1; then raise the diagonal entries in D (the eigenvalues of A) to the 29th power; and finally,evaluate the first component of PD29 P-1 to obtain F30.11:36 PM0 Type here to searchaRain...后 )4/26/2022(1

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The Fibonacci numbers are defined by Fo = 0, F = 1, Fx = Fx + Fk=1 for k = 1,2, .... Relations such as this are called recurrence relations or difference equations. We can recast this relation in "initial- value problem" form as follows: (Fr+1 Fr (*) - (; ) (^). (A) - O) k = 1,2,... FR- Fo It is apparent from this that (A)-( ) (A) k-1 k = 2,3, .... Find F30 as follows: First find the eigenvalues and associated eigenvectors of A := (}¿); next, find P, P¯1, and D that satisfy A = PDP-'; then raise the diagonal entries in D (the eigenvalues of A) to the 29th power; and finally, evaluate the first component of PD²9 p-1 to obtain F30- 1

The Fibonacci numbers are defined by Fo = 0, F = 1, Fx = Fx + Fk=1 for k = 1,2, .... Relations such as this are called recurrence relations or difference equations. We can recast this relation in "initial- value problem" form as follows: (Fr+1 Fr (*) - (; ) (^). (A) - O) k = 1,2,... FR- Fo It is apparent from this that (A)-( ) (A) k-1 k = 2,3, .... Find F30 as follows: First find the eigenvalues and associated eigenvectors of A := (}¿); next, find P, P¯1, and D that satisfy A = PDP-'; then raise the diagonal entries in D (the eigenvalues of A) to the 29th power; and finally, evaluate the first component of PD²9 p-1 to obtain F30- 1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 46E

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