Let to be the sequence defined by the 3rd order recursion relation tn+3 = 2tn+2 + tn+1 − 2tn, - for n ≥ 0, to = 1, t₁ = 2, t₂ = 3. Aun, (a) Convert the recursion relation into dynamical system of the form un+1 for a suitable matrix A and vectors un. Be sure to specify A, up and to relate the vectors un's to the tn's. = (b) Find the eigenvalues and eigenvectors of the matrix A of part (a), and use them to find a formula for un. (c) Use your solution of part (b) to find a formula for tn.
Let to be the sequence defined by the 3rd order recursion relation tn+3 = 2tn+2 + tn+1 − 2tn, - for n ≥ 0, to = 1, t₁ = 2, t₂ = 3. Aun, (a) Convert the recursion relation into dynamical system of the form un+1 for a suitable matrix A and vectors un. Be sure to specify A, up and to relate the vectors un's to the tn's. = (b) Find the eigenvalues and eigenvectors of the matrix A of part (a), and use them to find a formula for un. (c) Use your solution of part (b) to find a formula for tn.
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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Transcribed Image Text:Let to be the sequence defined by the 3rd order recursion relation
tn+3 = 2tn+2 + tn+1 − 2tn, for n ≥ 0, to = 1, t₁ = 2, t2 = 3.
Aun,
(a) Convert the recursion relation into dynamical system of the form Un+1
for a suitable matrix A and vectors un. Be sure to specify A, u。 and to relate the
vectors un's to the tn's.
=
(b) Find the eigenvalues and eigenvectors of the matrix A of part (a), and use them
to find a formula for un.
(c) Use your solution of part (b) to find a formula for tn.
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