The eigenvalues of the system(x +1]y" + 2xy' - 4y = 0 areA. None of themB. x = -i and x = iC. Å1 = -3 and Az = 4%3DD. A1 = -4 and Å = 2O E. x = -1 and x = 1%3D

Answered: The eigenvalues of the system + 1 ]y" +…

The eigenvalues of the system + 1 ]y" + 2xy' – 4y = 0 are O A. None of them B. x = -j and x = i C. A1 = -3 and = 4 D. Å1 = -4 and z = 2 E. x = -1 and x = 1

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: 3. Let A € Mn,n and let λ be an eigenvalue of A. Suppose A satisfies the equation 2A²+5A-10In Show…

Q: Find the eigen value andeigen vactor 3 -2 2. 56 -3

A: The given matrix is: A=3-2156210-3

Q: rify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. а13 -11, х, 3 (1, 2,…

Q: The eigenvalues of the system (+1"+2-4y = 0 are O A. A =-3 and = 4 %3D O B. x = -i and x = i O C. A1…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. 1q = 13, x, = (1,…

Q: Find the eigen values of A = |K [2 -3. a) 1 = -3,4 b) 1 = ±V7 c) 1 = 2+ V3 d) 1 = 3, -4 3.

Q: R 2. (a) Solve the equation sin¹(3x) = -x, giving the solution in an exact form.

Q: Using Eigenvalues and Eigen Vectors shve Cthe System: *C) =4メ+ y'4) =-2x *24 A=

A: Use the given matrix.

Q: .

A: Find the equation to express the Eigen values:

Q: Select the correct answer (s): The negation of the following statement is: "All perfect square are…

Q: Solve 1 . Find a particular solution to a' = x – y + e', y = -4x + y +t using undetermined…

Q: y" + 3y – 2x = 0 a' + y' – x = 0 (b) Express the as a first order system, and then find the eigen-…

A: Let the system of differential equation is, x1' =a1x1…

Q: When the eigenvalues of a b A = 0 d are 2, = 0 and 2, = 2, what are the possible values of a and d?…

A: When the eigen values of A=ab0dare λ1=0, and λ2=2, then to determine the possible values of a and d.…

Q: 5 2 22A: Find Eigen values for A = 2

Q: Exercise 6.2.1 For each system of ODE in (a)-(g), do the following: • Formulate the system as x =…

A: According to the guidelines, only one question and maximum three subpart can be answered. Please…

Q: Matrix ー45 -40 1. A= 68 59 has complex eigenvalues d= at ib cnd d2= a- ib where a = and b = O. The…

Q: Find the eigenvalues and bases for the eigenspaces of A³ for -2 -4 -4 A 2 4 2 -2 -2

Q: Suppose that i Ar. Draw the phase portrait where the 2 x 2 matrix A has %3D complex eigenvalue A =…

A: A phase portrait of a system of differential equation represents the directional behaviour of that…

Q: A 2x2 matrix is known to have the eigenvalues -3 and 4. What are the eigenvalues of the following…

A: We will find out the required value.

Q: [x =3x+2y y = 6x-y

A: Let X'=AX be a system of linear equations, then If the eigenvalues of A are positive , then critical…

Q: When the eigenvalues of a b *-[88] A = 0 d are ₁ = 0 and ₂ = 2, what are the possible values of a…

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: 21 2i with vi = -4 + 5i and = -2i with U2 -4 – 5i Write the general real solution for the linear…

Q: When the eigenvalues of a b A = 0 d are 11 = 2 and 12 = 0, what are the possible values of a and d?…

Q: 4. Find the eigenvalues and eigenvectors of A and A³, A-¹ and A - 21: [ A = 1 4 3 3

Q: a 14. If the complex number 3i is an eigenvalue of a matrix A = (d) a, b, c, d are real numbers,…

A: Solution:Given that, matrix and the eigenvalue of the matrix A is 3i.

Q: -6 2 |X -3 0 2. Find the eigen value of the system: X' =

A: To find the eigenvalue of the system:

Q: Verify that 1, is an eigenvalue of A and that x, is a corresponding eigenvector. 2 = -11, x, = (1,…

A: To verify that given eigenvalues and eigenvectors are belongs to the given matrix A.

Q: show that Hhe i'ntegraL equation g(s) -d scsinssinzt) g() 2t has No eigen values.a

A: The details calculation is given below

Q: What are the Eigenvalues of the system below: X' 1 -(-2²) 1 O 2+i, 2-i O 1,2 O 1+2i, 1-2i O +2i, -2i…

Q: 124 + 2452 + 35a3 + 24x4 = 24 356 + 24x2 + 35x3 + 754 = 2 241 + 56x2 + 35x3 + 67x4 = 47 256 + 87x2 +…

Q: Let vn = be the solution to the discrete dynamical system: Yn 6xn – 13yn Yn+1 = 0xn – 7yn Xn+1 -3 If…

A: Using diagonalisation of the coefficients matrix.

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: If a real first-order system defined by 1= Ax leads to complex eigenvalues r1,2 = a ±ßi in A, which…

Concept explainers

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.

Question

The eigenvalues of the system
(x +1]y" + 2xy' - 4y = 0 are
A. None of them
B. x = -i and x = i
C. Å1 = -3 and Az = 4
%3D
D. A1 = -4 and Å = 2
O E. x = -1 and x = 1
%3D

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

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Ellipses$

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

When the eigenvalues of a b A = are 1, = 3 and 1, = 0, what are the possible values of a and d? (Select all that apply.) O a = 0 andd = 3 O a = 0 and d = 0 O a = 3 andd = 3 %3D O a = -3 and d = 0 O a = 3 and d = 0 %3D O a = 0 and d = -3 %3D
-2 2. Find h in the matrix A = 7 such that the eigenspace for 1 = 7 is one- -1 4 -6 5 7 dimensional. Find h such that the eigenspace for 1=7 is two-dimensional.
Use (a) to solve the system x = (: :) . Х. -8 7 NB: Real solutions are required. Hint: Recall that if the roots of C(A) = 0 occur in complex conjugate parts, then any one of the two eigenvalues yields two linearly independent solutions. The second will yield solutions which are identical (up to a constant) to the solutions already found. a) is as follows Show from first principles, i.e., by using the definition of linear independence, that if x+iy, y # 0 is an eigenvalue of a real matrix A with associated eigenvector v = u + iw, then the two real solutions Y(t) = et (u cos bt – w sin bt) and Z(t) = eat (u sin bt + w cos bt) are linearly independent solutions of X = AX.
If the eigenvalues ofA 0. are A 6, A2 =-3, and dy = B then %3D OF 00 O a. B 2 Ob--1 O8=0 O d.=1 पि mittee
Q: Conficm by multiplicationthel cingenvector" of A, and find the collesponding l an eigenvalve. 1 2. 2. %3D 2.
In quantum mechanics, when two states with energies ₁ and E2 mix, the resulting states have different energies E and E, which are the eigenvalues of the matrix H = V (EK). V Choosing to be the state with higher energy, derive expressions for E + E, and E - E in terms of E1, E2 and V.