Given the 2 by 2 matrix A, find the eigenvalues and eigenvectors by hand, and if possible, the matrix X that diagonalizes it. That is, rather than using software, show details on how to find the characteristic equation det(A – I) = 0, find its roots, and plug them back in to find the eigenvectors. Then show how to use them to diagonalize the matrix (if possible) and use that to raise to a higher power, as in a Markov process. (a) A = L. 4 (b) A = 3
Given the 2 by 2 matrix A, find the eigenvalues and eigenvectors by hand, and if possible, the matrix X that diagonalizes it. That is, rather than using software, show details on how to find the characteristic equation det(A – I) = 0, find its roots, and plug them back in to find the eigenvectors. Then show how to use them to diagonalize the matrix (if possible) and use that to raise to a higher power, as in a Markov process. (a) A = L. 4 (b) A = 3
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 78E: Find all values of the angle for which the matrix A=[cossinsincos] has real eigenvalues. Interpret...
Related questions
Question
Please explain it step by step in detail. Thank you
![Given the 2 by 2 matrix A, find the eigenvalues and eigenvectors by hand, and if possible,
the matrix X that diagonalizes it. That is, rather than using software, show details on how to
find the characteristic equation det(A – A1) = 0, find its roots, and plug them back in to find
the eigenvectors. Then show how to use them to diagonalize the matrix (if possible) and use
that to raise to a higher power, as in a Markov process.
6.
(a) A = L4
4
(b) А %3
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d2fdd51-a813-4b36-89e9-f9581acfc2ee%2F4d8f8af3-b3b5-4a87-bc91-9878bcc9faa0%2Fcivkwco_processed.png&w=3840&q=75)
Transcribed Image Text:Given the 2 by 2 matrix A, find the eigenvalues and eigenvectors by hand, and if possible,
the matrix X that diagonalizes it. That is, rather than using software, show details on how to
find the characteristic equation det(A – A1) = 0, find its roots, and plug them back in to find
the eigenvectors. Then show how to use them to diagonalize the matrix (if possible) and use
that to raise to a higher power, as in a Markov process.
6.
(a) A = L4
4
(b) А %3
3
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.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Elementary Linear Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305658004/9781305658004_smallCoverImage.gif)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Elementary Linear Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305658004/9781305658004_smallCoverImage.gif)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781938168383/9781938168383_smallCoverImage.gif)