0 0 1 cos(0) -sin(@)) sin(0) cos(0) 1 1 (a) (c) 0 1 0 (d) -1 | 1 0 0
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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Question
![Due April 29, 2021
1. Find the eigenvalues and eigenvectors of the following matrices.
1
1
(4) ( D4
cos(0) -sin(0)
(b) (sin(e) cos(8)
1
(a)
V2
(c)
1 0
(d)
1
1
1
Which of the matrices in (a), (c), and (d) are non-degenerate? For which values of 0 € R is the
matrix in (b) degenerate?
2. Let m be a unit vector in R. Show that the eigenvalues of the 2 × 2 matrix om = mg0x+
myoy +mz0z are ±1, and that the corresponding eigenvectors are |m, ±).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d14b178-5b8c-4639-9880-9a6310b5f0da%2F7e7e903c-ef5f-4163-a2e1-cfe3ef01284b%2Fukw7wkk_processed.png&w=3840&q=75)
Transcribed Image Text:Due April 29, 2021
1. Find the eigenvalues and eigenvectors of the following matrices.
1
1
(4) ( D4
cos(0) -sin(0)
(b) (sin(e) cos(8)
1
(a)
V2
(c)
1 0
(d)
1
1
1
Which of the matrices in (a), (c), and (d) are non-degenerate? For which values of 0 € R is the
matrix in (b) degenerate?
2. Let m be a unit vector in R. Show that the eigenvalues of the 2 × 2 matrix om = mg0x+
myoy +mz0z are ±1, and that the corresponding eigenvectors are |m, ±).
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