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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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 57E
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] *CountAlg.java - Notepad e Edit Format View Help Ln 28, Col 1 100% Windows (CRLF) UTF-8 Problem 2. The Fibonacci numbers are defined by Fo = 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+1 1 Fk k = 1, 2, ... k-1 It is apparent from this that (2)-G )" (E). k-1 F1 (A). Fk 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-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. 1 1:36 PM 0 Type here to search a Rain... 后 ) 4/26/2022 (1
Transcribed Image Text:] *CountAlg.java - Notepad e Edit Format View Help Ln 28, Col 1 100% Windows (CRLF) UTF-8 Problem 2. The Fibonacci numbers are defined by Fo = 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+1 1 Fk k = 1, 2, ... k-1 It is apparent from this that (2)-G )" (E). k-1 F1 (A). Fk 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-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. 1 1:36 PM 0 Type here to search a Rain... 后 ) 4/26/2022 (1
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