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0 0 1 cos(0) -sin(@)) sin(0) cos(0) 1 1 (a) (c) 0 1 0 (d) -1 | 1 0 0

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
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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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, ±).
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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