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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
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