Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
-a (1) Let a, b, t E R, and a + b # 0. A = a b What is the expression of e4t? What are the eigenvalues and the coresponding eigenvectors of e4At?

-a (1) Let a, b, t E R, and a + b # 0. A = a b What is the expression of e4t? What are the eigenvalues and the coresponding eigenvectors of e4At?

Advanced Engineering Mathematics
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
icon
Related questions
Question

  1. (1)  Let ?, ?, ? ∈ R, and ? + ? ≠ 0. ? = [−? ? ]. What is the expression of ???? What are the ? −?

    eigenvalues and the coresponding eigenvectors of ????

  2. (2)  ? ∈ R5×5. Its characteristic polynomial is ?(?) = (? − 2)3(? + 3)2 and its minimal polynomial is ??(?) = (? − 2)2(? + 3)1. Write the Jordan form of ?, and the details your derivation. (Notice that the minimal polynomial of a square matrix A is a polynomial that divides the characteristic polynomial of ? and vanishes at ?.)

Problem2: (1) Let a, b, t E R, and a + b # 0. A =| PJ. What is the expression of e At? What are the а eigenvalues and the coresponding eigenvectors of e 4t? (2) A E R5×5. Its characteristic polynomial is p(s) = (s – 2)³ (s + 3)2 and its minimal polynomial is Pm(s) = (s – 2)²(s + 3)'. Write the Jordan form of A, and the details your derivation. (Notice that the minimal polynomial of a square matrix A is a polynomial that divides the characteristic polynomial of A and vanishes at A.) |
Transcribed Image Text:Problem2: (1) Let a, b, t E R, and a + b # 0. A =| PJ. What is the expression of e At? What are the а eigenvalues and the coresponding eigenvectors of e 4t? (2) A E R5×5. Its characteristic polynomial is p(s) = (s – 2)³ (s + 3)2 and its minimal polynomial is Pm(s) = (s – 2)²(s + 3)'. Write the Jordan form of A, and the details your derivation. (Notice that the minimal polynomial of a square matrix A is a polynomial that divides the characteristic polynomial of A and vanishes at A.) |
Expert Solution
steps

Step by step

Solved in 7 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS