[-Ha. For the initial condition x(0) =Consider the system x = Ax with A =0-31calculate x, (t) and x₂ (t).b. Find the eigenvalue(s) and the eigenvectors (or generalized eigenvector) of thematrix A.c. Consider each eigenvector (or generalized eigenvector) as initial condition andcalculate x₁ (t) and x₂(t).

Answered: Image /qna-images/answer/38bc200a-830e-43fd-afae-7452777e4cf7.jpg

Answered: Consider the system x = Ax with A = 0…

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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A 2x2 upper triangular matrix A has eigenvalues a and - 5 (with a ≠ -5). An eigenvector corresponding to the eigenvalue a is (1,0). Which of the following could be the matrix A? A. (-5 a/2 0) B. (a 0/2 -5) C. (-5 2/0 a) D. (a -5/0 2) E. (a 2/0 -5)
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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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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