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
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 12E: Suppose that the check digit is computed as described in Example . Prove that transposition errors...
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