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Let M be a 2 x 2 matrix with eigenvalues A1 = -0.9, A2 :-0.75 with corresponding eigenvectors - [고. V1 V2 Consider the difference equation Xk+1 = Mx with initial condition xo Write the initial condition as a linear combination of the eigenvectors of M. That is, write xo = c¡V1 + C2V2 Vi+ V2 In general, X Vị+ Specifically, x2 : For large k, Xk →

Let M be a 2 x 2 matrix with eigenvalues A1 = -0.9, A2 :-0.75 with corresponding eigenvectors - [고. V1 V2 Consider the difference equation Xk+1 = Mx with initial condition xo Write the initial condition as a linear combination of the eigenvectors of M. That is, write xo = c¡V1 + C2V2 Vi+ V2 In general, X Vị+ Specifically, x2 : For large k, Xk →

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 A1 = -0.9, A2 =-0.75 with corresponding eigenvectors V1 V2 Consider the difference equation Mx: with initial condition xo Write the initial condition as a linear combination of the eigenvectors of M. That is, write xo = ¢¡V1 +C2V2 Vi+ V2 In general, X Vi+ )* v2 Specifically, x2 For large k, Xk →
Transcribed Image Text:Let M be a 2 x 2 matrix with eigenvalues A1 = -0.9, A2 =-0.75 with corresponding eigenvectors V1 V2 Consider the difference equation Mx: with initial condition xo Write the initial condition as a linear combination of the eigenvectors of M. That is, write xo = ¢¡V1 +C2V2 Vi+ V2 In general, X Vi+ )* v2 Specifically, x2 For large k, Xk →
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