8. Given the systemdxdt22A=²2₁5 -1= Ax with A(a) Find the eigenvalues and corresponding eigenvectors associated with A.Write as eigenpairs.(b) Give a general solution to the system.(c) Give an invertible matrix V and diagonal matrix D that diagonalizes A(d) Compute eta(e)Sketch its phase plane portrait, indicating typical orbits. Describe thestability of the origin.

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Answered: 8. Given the system dx dt = = Ax with…

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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8. Given the system dx dt = = Ax with A= 22 5 -1 (a) Find the eigenvalues and corresponding eigenvectors associated with A. Write as eigenpairs. (b) Give a general solution to the system. (c) Give an invertible matrix V and diagonal matrix D that diagonalizes A at A