a) Find all eigenvalues and eigenvectors forA = ; )\4 -2.b) Find the general solution todx:2х — уdtdy— 4х — 2уdt

Answered: Image /qna-images/answer/500f7372-2196-4472-9223-20fc0f0a834a.jpg

Answered: a) Find all eigenvalues and…

Math

Advanced Math

a) Find all eigenvalues and eigenvectors for A = (; ) 4 b) Find the general solution to dx 2х — у dt dy 4x — 2у dt

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Find all solutions of the following system of linear equations: dx dt = 4x + 8y, dy dt Xg = C1 = -2x - 4y Hi, I have to ask this question for the third time because the answers given were incomplete. Here, eigenvalue 0 is a repeated eigenvalue. So, answer includes two eigenvectors of corresponding eigenvalue, 0. Could you also show me how can I find the second eigenvector of it? Answer key says that the answer is: [1] +0₂² [2¹] -0₂H] 1-2
Compute the other eigenvector. And draw each of the eigenvectors and the transformed vectors (with A) on the graph below.
a) Find the eigenvalues of A. b) Find three linearly independent solutions of x' = Ax. c) Find the exponential e^(tA) Let A = 2 -1 ا دیا 0 0 3 0 -30
Use the eigenvalue method to solve the following system T = *1 + T* 2, 2
f2 f3 14 Let A = 2. 1- find the eigenvalues of A. OM
0 4 V = 4V is: 13 Question (4 points) Eigenvector V satisfying Select one: t> 1>
Evaluate the resultant function when v operates on sin(-3x) + cos(3y) where d? d? dx? dy? b) Is sin(-3x) + cos(3y) an eigenfunction of v²? If yes, report the eigenvalue.
5) Find the values of that such that the given equations have non-trivial solutions. What are the eigenvalues and eigenvectors? (1-2) x + 2y = 0 2x + (4-2)y=0
For the system of differential equations, X1, X2 a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. U₁ = U2 = = y' = c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller eigenvalue X₁ and u2 is the eigenvector associated with the larger eigenvalue A2. 5 2 - 1 Y2 (t) d) Determine two linearly independent solutions to the system. Enter the first solution in the format y₁ (t) y = = y₁ (t) Enter the second solution in the format y₂(t) = ƒ2(t) (v3h₁(t) + v₁h₂(t)) = : fi(t) (vigi(t) – v2g2(t)) . +
Q: Conficm by multiplicationthel cingenvector" of A, and find the collesponding l an eigenvalve. 1 2. 2. %3D 2.
Find the eigenvalues and the eigenvectors of A and A-1 (check the trace!): A λι = X2 = 2 A-1 = [ -0.5 11 0.5 ]: λι = with x1 = and 9. with x2 = with x1 = and 9. X2 = with x2 =
Matrix A has the eigenvalue 2 = 5 and eigenvector v. Find generalized eigenvector. 7 1 01 1|,λ5, ν = A = -3 4 -2 1 41 X2=