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Consider the difference equation with initial condition Xo = That is, write xo = c1v1 + c2V2 In general, x = Write the initial condition as a linear combination of the eigenvectors of M. Specifically, x5= For large k, xk → ( V1+ V1 = )k vit 2 Xk+1 = V2 ( V2 = Mxk )k V2

Consider the difference equation with initial condition Xo = That is, write xo = c1v1 + c2V2 In general, x = Write the initial condition as a linear combination of the eigenvectors of M. Specifically, x5= For large k, xk → ( V1+ V1 = )k vit 2 Xk+1 = V2 ( V2 = Mxk )k V2

Advanced Engineering Mathematics
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 X₁ = -0.3, A2 = 0.75 with corresponding eigenvectors 2 --4--4- , V2 = Consider the difference equation with initial condition xo = 11 Write the initial condition as a linear combination of the eigenvectors of M. That is, write x0 = c1v1 + c2V2 = In general, x = Specifically, x5 = For large k, xk → V1+ V1 = )kv₁+ Xk+1= Mxk V2 )k V2
Transcribed Image Text:Let M be a 2 x 2 matrix with eigenvalues X₁ = -0.3, A2 = 0.75 with corresponding eigenvectors 2 --4--4- , V2 = Consider the difference equation with initial condition xo = 11 Write the initial condition as a linear combination of the eigenvectors of M. That is, write x0 = c1v1 + c2V2 = In general, x = Specifically, x5 = For large k, xk → V1+ V1 = )kv₁+ Xk+1= Mxk V2 )k V2
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