Consider a system 7'a) Find the eigenvalues of A.b) What is the type of the Phase-Plane portrait ? Is the origin attractingor repelling, or neither attracting nor repelling ? Is the origin stable ?c) Find eigenvectors. Then use eigenvalues and eigenvectors to write a gen-A and answer the following questions.eral solution.d) Use any method to find the matrix exponential etA.e) Find the solution of the given initial value problem.f) In the phase plane sketch eigenlines and sketch the solution curve 7(t), –∞ <t < o, of the IVP. DO NOT sketch other solution curves.Clearly show two parts of your curve : one corresponding to t > 0,corresponding to t < 0. Use arrows to show the direction of increasing t onthe curve and on the eigenlines. Mark the point (0). Evaluate the tangentvector to the solution curve at (0) and sketch it.another()T , 7(0) =31

Hi, since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Consider a system a' = Ax and answer the following questions. a) Find the eigenvalues of A. b) What is the type of the Phase-Plane portrait ? Is the origin attracting or repelling, or neither attracting nor repelling ? Is the origin stable ? c) Find eigenvectors. Then use eigenvalues and eigenvectors to write a gen- eral solution.

Consider a system a' = Ax and answer the following questions. a) Find the eigenvalues of A. b) What is the type of the Phase-Plane portrait ? Is the origin attracting or repelling, or neither attracting nor repelling ? Is the origin stable ? c) Find eigenvectors. Then use eigenvalues and eigenvectors to write a gen- eral solution.

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

Related questions

Q: (a) Find all eigenvalues of A. (b) Show that 7 = 0 is the only equilibrium solution of the system.…

Q: (b) A = 3 is an eigenvalue of A. Find an eigenvector of A with this eigenvalue. (c) The matrix A is…

Q: Fnd the elgen functins Unckl tor nzl . for of the eigen functien problem. y13)=0

Q: determine the eigenvalues and eigenvectors if the eigenvalues are real (or use results from…

A: To find the eigenvalues of the given system, we will write the system in matrix form as follows:…

Q: Each linear system has complex eigenvalues. For each system, (a) find the eigenvalues; (b) determine…

Q: determine the eigenvalues and eigenvectors if the eigenvalues are real

A: In this question, we find the eigenvalues and eigenvector for the given linear system. Also we find…

Q: In Exercises 1–4, each of the linear systems has one eigenvalue and one line of eigen- vectors. For…

A: Note: As per Bartleby's guidelines, for more than one question asked in the main part and for more…

Q: 7. Find the eigenvalues and eigenvectors of the following linear systems: a) b) 2x1 + 3x2= x1 4x1 +…

A: a) 2x1+3x2= λx1 4x1+3x2= λx2b) 3x1+x2 = λx1 -5x1-3x2= λx2

Q: a) Find the eigenvalues and eigenvectors of the ma- 1 2 M 0 -1 -2 %3D 2 -2 Order your eigenvalues so…

Q: dx -5х — у, dt dy — 3х — у. dt

Q: Let A = -2 10 2. One of the eigenvalues of A is X = 2. 020 -1 4 1 a) Find a basis for the eigenspace…

A: Given: A=-2102020-141, λ1=2 To find (a) Basis for the eigenspace of A associated with λ=2. (b) Other…

Q: Each of the linear systems has one eigenvalue and one line of eigenvectors. For each system, (a)…

Q: To every eigenvaluebof a sturm liouville system there corresponds only one linearly independent…

Q: The eigenvalues of A will be complex conjugates. Analyze the stability of equilibrium (0,0). Is it a…

Q: A) Find the Eigenvalue and Eigenvector B) Classify the critical point (0,0) and state if it's stable…

A: Given system of differential equation

Q: The eigenvalues of A will be complex conjugates. Analyze the stability of equilibrium (0,0). Is it a…

A: To find- The eigenvalues of A will be complex conjugates. Analyze the stability of equilibrium 0, 0.…

Q: Match pairs of eigenvalues to the phase portraits of two dimensional systems. A₁ = -1, A₂=-2…

A: To match the phase portraits of the given eigen values:1). If both the eigen values are of same sign…

Q: Show A has the repeated eigenvalue?

Q: a) x = 3x + 2y y = -y b)x = 5x + 4y y = 3x + y

Q: determine the eigenvalues and eigenvectors if the eigenvalues are real (or use results from…

A: For finding the eigenvalues of the given system, we can write the system as follows:…

Q: (a) compute the eigenvalues; (b) for each eigenvalue, compute the associated eigenvectors; () using…

Q: Match pairs of eigenvalues to the phase portraits of two dimensional systems. ₁1,4₂ = 2 4₁=-1, 4-2…

A: To match the phase portraits of the given eigen values:

Q: etermine the equation of your model that will pass 2,4

A: We already have the equation of polynomialand

Q: Suppose that a surface contains a straight line. Explain why, for any point in this line, the second…

A: Suppose that the second fundamental form of a surface patch is zero everywhere. We Prove that is…

Question

Consider a system 7'
a) Find the eigenvalues of A.
b) What is the type of the Phase-Plane portrait ? Is the origin attracting
or repelling, or neither attracting nor repelling ? Is the origin stable ?
c) Find eigenvectors. Then use eigenvalues and eigenvectors to write a gen-
A and answer the following questions.
eral solution.
d) Use any method to find the matrix exponential etA.
e) Find the solution of the given initial value problem.
f) In the phase plane sketch eigenlines and sketch the solution curve 7(t), –∞ <
t < o, of the IVP. DO NOT sketch other solution curves.
Clearly show two parts of your curve : one corresponding to t > 0,
corresponding to t < 0. Use arrows to show the direction of increasing t on
the curve and on the eigenlines. Mark the point (0). Evaluate the tangent
vector to the solution curve at (0) and sketch it.
another
()
T , 7(0) =
3
1

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step by step

Solved in 6 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Matrix Eigenvalues and Eigenvectors$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Suppose we are modeling the spread of a disease. People are categorized as either susceptible or infectious (similar to our Module 7 discussion board). Those who are susceptible do not have the disease, but could get it. Those who are infected currently have the disease. We assume this disease is not transmittable by contact with an infectious person. Instead, we will assume it is something that is contracted through environmental factors. Define: dt = -.035.S = .03S - .021 where . S = number of the people in the population who are susceptible I= number of the people in the population who are infected t = time since outbreak observed, days NOTE: Here we are dealing with the number of people, rather than the proportion of people, in each group. This fact should not change your analysis in any significant way. Anyone who is not susceptible or infected falls into a third category: immune. We do not concern ourselves with this group, because they are people who cannot get the disease…
4. Find the eigenvalues for the matrix :) 1 -1 A = 1 2 1 -2 1 -1 For any one of these eigenvalues, find a specific corresponding eigenvector.
(4) Eigenvectors that correspond to distinct eigenvalues could be linearly de- pendent.
Let 2. 1 -1 D= 0 3 -1 0 0 2 a. Find the eigenvector(s) associated with the eigenvalue X = 2 1 b. Is the vector an eigenvector of D? Why or why not? 3 c. Based on your work so far do you know if D is diagonalizable? Why or why not.
The eigenvalues of A will be complex conjugates. Analyze the stability of equilibrium (0,0). Is it a stable spiral, an unstable spiral, or a center? A= [ 0 -1] [1 -1]
determine the eigenvalues and eigenvectors if the eigenvalues are real (or use results from exercises from Section 4.2. if you have covered those exercises). Also classify the system (state whether stable or unstable node, stable or unstable spiral, center, saddle point) and in all cases sketch the phase plane of the linear system. (As a hint, problems with * have complex eigenvalues.) When checking your answers with those in the back of the book, keep in mind that any nonzero multiple of the given eigenvector may be used.
a) Find the characteristic equation. b) Find the eigenvalues of A. c) Is the matrix A diagonalizable? Why?
The eigenvalues in this problem are all nonnegative. First determine whether A=0 is an eigenvalue; then find the positive eigenvalues and associated eigenfunctions. 7y +Ay=0; y(-x)=0, y(x)=0 Is A = 0 an eigenvalue of this problem? Select the correct answer below and, if necessary, fill in the corresponding answer box to complete your choice. OA. Yes, A-0 is an eigenvalue with the corresponding eigenfunction yo(x)= OB. No, when A=0 the only solution to the given equation is the trivial solution. OC. No, when A=0 there are an infinite number of nontrivial solutions to the give equation. What are the eigenvalues and eigenfunctions of the problem for n=1. 2. 3...? Select the correct answer below and fill in the corresponding answer box to complete your choice OA. The eigenvalues are À = OB. The eigenvalues are À = The eigenfunctions are yn(x)= The eigenfunctions are y(x) = regardless of whether n is even or odd when n is even and y(x) when n is odd.