22) Solve the following system of ODEs by computing the eigenvalues and eigenvectors of thecoefficient matrix A:where3A = 0dXdt= AX+b001/2-3/20 -3/2 1/2subject to the following generic initial condition:Xº =b= 2What are admissible initial conditions, Xº, if as t→∞, X remains bounded (i.e., X<∞0).Write down the general form of the initial conditions.

Answered: Image /qna-images/answer/9b97c708-7af5-4d67-a7c9-4b59605deea3.jpg

Answered: 2) Solve the following system of ODEs…

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

VII. Run two iterations using normalized power iteration method for the following matrix and initial vector. Roughly predict the dominate eigenvalue and corresponding eigenvector. A = [ ²₁ 2] ₁ x₁ = 1 []
10. (BH) Let L : P + P2 be defined by L(p(e)) = zp'(2) dz, and let E = {1,t} and E2 = {1,t, t} be the standard bases for Pi and P2. (a) Find the matrix A associated with in these bases. (b) Find £(3t – 1) directly and using A.
31. (a) Let A be an n × n-symmetric matrix. Diagonalize A to show that x • Ax 2 || x || ² is greater than or equal to the smallest eigenvalue of A for all x # 0 in R". (b) Show that the quadratic form Q₁(x) = x Ax is coercive if and only if A is positive definite. (c) Conclude from (b) that if f(x) = a + b x + 1x. Ax is any quadratic function where a = R, be R₁ and A is an n - n-symmetric matrix, then f(x) is coercive if and only if A is positive definite.
q7
6. Consider the matrix A = Compute the eigenvalues of A, and the corresponding eigenspaces.
5. Let A be a 6 x 6 matrix with characteristic equation X2(a – 1) (A – 2)3= 0. What are the possible dimensions for eigenspaces of A?
4. Let At be a matrix that depends on r and is given by At t 3 -2 1 (a) For which te R matrix At has no real eigenvalues for At? (b) For which t E R matrix At has exactly one real distinct eigenvalue? Give that eigenvalue. (c) For which te R matrix At has two different real eigenvalues? Give one such eigenvalue as a function of t.
4. A real, symmetric 3-by-3 matrix M has eigenvalues X₁ = 4, X₂ 1 vector corresponding to the eigenvalue X₁ = 4 is v₁ -1 0 [4] -2 to the eigenvalue X₂ = 6 is v₂ = 6 and X3 = -3. An eigen- and an eigenvector corresponding What is M?
Suppose that a 2 x 2 matrix A with real entries has an eigenvalue X = 1 + 3i with corresponding 4 i [12] eigenvector 1 + 2i Which of the following is NOT a solution of the linear system y' = Ay? y(t) = et y(t) = et y(t) = et y(t) = et 4 cos(3t) sin(3t) [cos(3t) + 2 sin(3t). 4 cos(3t) + sin(3t) cos(3t) 2 sin (3t) - cos(3t) + 4 sin(3t) 2 cos(3t) + sin(3t) cos (3t) - 4 sin (3t) -2 cos(3t) - sin(3t)
7. Let the 2 x 2 matrix A have real, distinct eigenvalues and μ. Suppose that an eigenvector of A is (1,0)" and an eigenvector of u is (-1,1)". Sketch the phase portraits of is x = Ax for the following cases: (1) 0 0. وچستان ستان ج
I 74 la * 5. Let T'is a matrix of iterative method for solving linear system Ax b. If A is a positive definite and tridiagonal matrix, then p(T) is equal to (b) [p(Ta)12 (d) None of the above. (a) √p(TG) (c) p(Ta) a d 6. The absolute norm for tensor of two eigenvectors of A = = (-_-³₁-3) is (b) √3 (d) None of the above. (a) 0 9:06 ص 2 A A (c) √2 a

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS