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2X2 matrix with eigenvalues A₁ =-1.2, A2 = 1 with corresponding eigenvectors Consider the difference equation with initial condition Xo= [3]. V₁ = V2 Xk+1 = MX Write the initial condition as a linear combination of the eigenvectors of M. That is, write Xo = c1V1 + C2V2= In general, Xk= V₁+ V2 )* VI+ Specifically, X4=

2X2 matrix with eigenvalues A₁ =-1.2, A2 = 1 with corresponding eigenvectors Consider the difference equation with initial condition Xo= [3]. V₁ = V2 Xk+1 = MX Write the initial condition as a linear combination of the eigenvectors of M. That is, write Xo = c1V1 + C2V2= In general, Xk= V₁+ V2 )* VI+ Specifically, X4=

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 × 2 matrix with eigenvalues ₁ = -1.2, A2 = 1 with corresponding eigenvectors Consider the difference equation with initial condition Xo = 5 3 V₁ = V2 = 2 xk+1 = Mxk Write the initial condition as a linear combination of the eigenvectors of M. That is, write x0 = c1V1 + C₂ V₂ = In general, xk= V1+ V2 ) * vi+ k ) v2 Specifically, x4 = For large k, xk≈ k
Transcribed Image Text:Let M be a 2 × 2 matrix with eigenvalues ₁ = -1.2, A2 = 1 with corresponding eigenvectors Consider the difference equation with initial condition Xo = 5 3 V₁ = V2 = 2 xk+1 = Mxk Write the initial condition as a linear combination of the eigenvectors of M. That is, write x0 = c1V1 + C₂ V₂ = In general, xk= V1+ V2 ) * vi+ k ) v2 Specifically, x4 = For large k, xk≈ k
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