trix
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
![Consider the matrix A =
-1/2 1/2
-1/2 -1/2]
(a) Find the eigenvalues of A and calculate p(A).
(b) What can you say about lim Ak?
k→∞
(c) Find an invertible matrix T and diagonal matrix D such that A = TDT-1. Note: the matrices
T and D will have complex entries. Compute T-1 and verify by direct multiplication that A =
TDT-¹.
=
007-34](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffc06da2-7bd8-42a3-b8a1-3f8b831a8034%2F3103ec9b-9030-45b9-a796-57c868eb76a9%2F4dtsajj_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the matrix A =
-1/2 1/2
-1/2 -1/2]
(a) Find the eigenvalues of A and calculate p(A).
(b) What can you say about lim Ak?
k→∞
(c) Find an invertible matrix T and diagonal matrix D such that A = TDT-1. Note: the matrices
T and D will have complex entries. Compute T-1 and verify by direct multiplication that A =
TDT-¹.
=
007-34
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