Problem 4. Let A =You are given that (2 – A) ( –- X) is the characteristic510polynomial of A.Find the eigenspace E2.Without any more calculation, find the eigenspace E1.Sketch the phase portrait for the discrete dynamical system 7(t + 1) = AF(t).Describe all possible ão for which lim00 7(t) = lim;→∞ A'ão equals 0.Let A = A+ kI2. Consider the discrete dynamical system ī(t+1) = Ak7(t).(b)For which k is 0 an asymptotically stable equilibrium for this system?

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Answered: 4 Problem 4. Let A You are given that…

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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6. (a) Let T : L²[0, 2π] → L²[0, 2ñ] be given by 2π Tf(x) = s cos(xt) f(t) dt. Show that (i) T is self-adjoint. (ii) cos x and sin x are eigenvectors of T.
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(a) Show that the function Cos(nx) is the eigenfunction of the operator A What is = - 2 dx2 the eigenvalue of this eigenfunction? (b) Define two operators P = and X =2x, which means P f(x) = f(x) = f'(x), 8 f(x) = 2xf(x). Are these two operators commutable? [hint: for any f (x), compute P8 f(x) and X Pf(x), and compare results.)

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4 Problem 4. Let A You are given that (2 – A) ( –1) is the characteristic 10 polynomial of A. (a) (b) (c) Find the eigenspace E2. Without any more calculation, find the eigenspace E1. Sketch the phase portrait for the discrete dynamical system 7(t + 1) = AF(t).