Let M be a 2 x 2 matrix with eigenvalues A₁ = 0.3, A2= -0.25 with corresponding eigenvectors = [2²] ²2² = [9] · V₂ Consider the difference equation with initial condition Xo That is, write xo = C1V1 + C₂V2 H Write the initial condition as a linear combination of the eigenvectors of M. In general, x Specifically, X4 V1 = For large k, xk Xk+1 = V₁+ )k v₁+ Mxk T V2
Let M be a 2 x 2 matrix with eigenvalues A₁ = 0.3, A2= -0.25 with corresponding eigenvectors = [2²] ²2² = [9] · V₂ Consider the difference equation with initial condition Xo That is, write xo = C1V1 + C₂V2 H Write the initial condition as a linear combination of the eigenvectors of M. In general, x Specifically, X4 V1 = For large k, xk Xk+1 = V₁+ )k v₁+ Mxk T V2
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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![Let M be a 2 x 2 matrix with eigenvalues A₁ = 0.3, A2 = -0.25 with corresponding eigenvectors
= [2²] ²2² = [9] ·
V2
Consider the difference equation
with initial condition xo
That is, write xo = C1V1 + C₂V2
H
Write the initial condition as a linear combination of the eigenvectors of M.
In general, X =
Specifically, X4
V1 =
For large k, xk
Xk+1 =
V₁+
)k v₁+
Mxk
A
V2
7)k V₂](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8a6a219-8dd6-4363-b3bc-2b1c314a775e%2Ff872e4c3-7f7f-4c38-a0c5-0d5be5e85f77%2Fv4uetiq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let M be a 2 x 2 matrix with eigenvalues A₁ = 0.3, A2 = -0.25 with corresponding eigenvectors
= [2²] ²2² = [9] ·
V2
Consider the difference equation
with initial condition xo
That is, write xo = C1V1 + C₂V2
H
Write the initial condition as a linear combination of the eigenvectors of M.
In general, X =
Specifically, X4
V1 =
For large k, xk
Xk+1 =
V₁+
)k v₁+
Mxk
A
V2
7)k V₂
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