Please answer letter B. Thank you. a) Show that x₁ * = y₁= x₂ * = y₂ = u is a fixed point for all choices of parame-ters and that u is uniquely defined.b) Show that the stability matrix (the Jacobian) for the linearization about thisfixed point has the form-C₁-C₂-C30d₁ -d₁ 0 0-C3 0 -C₁-C₂00 d₁ -d₁)We can write this in block-matrix form as(A B)BAwhere A and B are 2x2 matrices. Show that the four eigenvalues of the 4×4block matrix are given by the eigenvalues of A-B and A+B.

Consider the matrix .To Find:Show that the stability matrix for the linearization about this fixed…

b) Show that the stability matrix (the Jacobian) for the linearization about this fixed point has the form -₁ -₂ -₂ d, -d, 0 0 0 -9-9₂ d, -d₁) We can write this in block-matrix form as 0 0 0 (A B BA where A and B are 2x2 matrices. Show that the four eigenvalues of the 4x4 block matrix are given by the eigenvalues of A-B and A+B.

b) Show that the stability matrix (the Jacobian) for the linearization about this fixed point has the form -₁ -₂ -₂ d, -d, 0 0 0 -9-9₂ d, -d₁) We can write this in block-matrix form as 0 0 0 (A B BA where A and B are 2x2 matrices. Show that the four eigenvalues of the 4x4 block matrix are given by the eigenvalues of A-B and A+B.

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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