xtLet xt and y(t) be c functions on R and let zit)= . Let A be a 2x2 real constant matrix such that z'(t)= Az(t) for all tER. Let à be aneigenvalue of A with corresponding eigenvector v, then a solution for zit) isexpižajovλexp λt-vexp(-at-vexp iat - v

Answered: Image /qna-images/answer/61394eb0-3df0-4a63-9439-43faf582181f.jpg

Answered: Let xit) and y(t) be c functions on R…

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) Let matrix A have eigenvectors . . associated with eigenvalues Xo = 4, A₁ = 2, A₂ = 0), respectively. Suppose some vector 7 is: 7 = №n +27₁ +30¹₂ Compute Ar. Give your result as a linear combination of eigenvectors ₁.
Let the eigenvalues of the matrix A be A1, A2, . . A,n and the linearly w m w w w w w ma ndependent eigenvectors corresponding to these eigenvalues V1,V2,.. Vn. .... ww m ww (S [V1V2 . .. Vn]nxn) || by placing the vectors V1,V2,., Vn in each column of A is the eigenvalue of V1,V2,.., Vn placed on the w w m w m w w the S matrix; If the matrix diagonal, prove that, diagonal matrix. Also show that eAt mw wm m m w ww diag[A1 A2 . .. A,]nxn) with in the A = SAS-1 (A SeAt s-1 . %3D ww w w w w m
Let M be a 2 × 2 matrix with eigenvalues ₁ = -1.2, A2 = 1 with corresponding eigenvectors Consider the difference equation with initial condition Xo = 5 3 V₁ = V2 = 2 xk+1 = Mxk Write the initial condition as a linear combination of the eigenvectors of M. That is, write x0 = c1V1 + C₂ V₂ = In general, xk= V1+ V2 ) * vi+ k ) v2 Specifically, x4 = For large k, xk≈ k
Let A be a arbitrary n x n matrix, Show that if A1 and A2 are two eigenvalues with A1 # ^2 and eigenvectors vi and v2, respectively. Show that vị and v2 are linerly independent.
Let B be a 3x3 matrix with eigenvalues 0,1,2. Then, the eigenvalues of BB T is (Hint: B and BT have the same eigenvalues) only 0 0,1,2 0,1,4 1,4
Find the eigenvalues of the matrix Smaller eigenvalue = Associated eigenvector = Larger eigenvalue = Associated eigenvector = -12 -8 40 24 Note: vectors are entered with "angle brackets", such as or .
If A is a 3 x 3 matrix with Eigen values, x, y, z then the Eigen values of A'are 1 1 1 (a) y.z (b) -х, -у,-2 (с) (d) x. y.z
Suppose A + u are distinct eigenvalues of A, with corresponding eigenvectors u and v. (Au)™v = Au" v O pu"v V O du7v (Check ALL that apply) uv = are column vectors corresponding to the vectors u, v, then u'v is a Prove your result. Suggestion: If u, matrix whose entry is i · v.
If a matrix R satisfies that RTR = I, show that the column vectors of R are orthonormal. LG

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

Let xit) and y(t) be c functions on R and let zt=xt . Let A be a 2x2 real constant matrix such that z't=Azt for all tER. Let à be an eigenvalue of A with corresponding eigenvector v, then a solution for zit is expizdev λexp λt-v exp-λt-v exp int).v