-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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
-
(1) Let ?, ?, ? ∈ R, and ? + ? ≠ 0. ? = [−? ? ]. What is the expression of ???? What are the ? −?
eigenvalues and the coresponding eigenvectors of ????
-
(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.)
|](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab98da9c-b172-423a-b74f-4a148099c4c1%2F19425037-9ec5-43d6-9fa6-bb6ec8c49e9f%2Fphclvjm_processed.png&w=3840&q=75)
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
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 7 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)