7. Let the 2 x 2 matrix A have real, distinct eigenvalues and μ. Suppose that aneigenvector of A is (1,0)" and an eigenvector of u is (-1,1)". Sketch the phase portraits ofis x = Ax for the following cases:(1) 0 < <(b) (0 < <(e) < 0 <(d) 1 < 0 <( < < 0(f) A = 0, > 0.وچستانستان ج

Given : The 2 × 2 matrix A have a real, distinct eigenvalues λ' and μ. An eigenvector of λ is 1 , 0T…

Answered: and μ. Suppose that an 7. Let the 2 x 2…

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

3 *. Sketch a graph of the eigenvectors and plot Solve the system of ODES given by i' = | , some sample trajectories. Is the origin an attractor, a repeller or a saddle point? -2.
Let x(t) x₁ (t) x' (t) x₁ (t): = = If x (0) = x₂(t): = = = ] Put the eigenvalues in ascending order when you enter x₁ (t), x₂(t) below. exp( t) + exp( x₁(t) x₂(t) -27 x₁(t) + 12x₂(t) -56 x₁(t) + 25 x₂(t) 4 be a solution to the system of differential equations: -2 exp( find x(t). t) + exp( t) t)
1 Let P = -2 - Find p P. Deduce P, if it exists, from the result of -1 p' P. You can also calculate P 1 using the traditional approach but this will be slower. 2. Let A be a 3 x 3 matrix with the following eigen-pairs: 1 (1, ):(1, 0 ):G -2 ).
Find the smallest eigen value of (1+x)y" + y' + λy = 0, y(0)=0, y(1)=0
lloa [Ur ses SEC::116 Question 9 Find the general solution to the system x' = Ax where A is the given matrix. -2 -1 1 A= -1 -9 3 -1 -2 -4 Hint: -6 is an eigenvalue.
Let A be a 2 x 2 matrix with eigenvalues X₁ = -3 and >₂ = -1 and [1] an H Let x(t) be the position of a particle at time t. Suppose we solved the initial corresponding eigenvectors V₁ = value problem x = Ax, x(0) = [3] -ce + c₂e-t x(t) = = [2(t)] = [ qe * +ge + -3t Search and C2= -3t and V2 = to obtain then C1=
Show your work
Solve the system of ODES given by x' x. Sketch a graph of the eigenvectors and plot 13 some sample trajectories. Is the origin an attractor, a repeller or a saddle point? Give your final solution in exact form with e.
sin z 3. Let A = COS I - sin z Show that A-= A". COS I For which values of z has this matrix real eigenvalues?
Q7

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

and μ. Suppose that an 7. Let the 2 x 2 matrix A have real, distinct eigenvalues eigenvector of λ is (1,0)7 and an eigenvector of u is (-1,1). Sketch the phase portraits of is x = Ax for the following cases: (a) 0 <^<μ (d) λ <0<μ (b) 0 <µ 0.