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Find the characteristic equations of the following matrices: (a) 1] -2 1 0 -2 0 1 4 0 0 -5 (b) | 3 1 - -1 1 -2 (c) -2 -6 -2 1 19 5 5 -4 1.

Find the characteristic equations of the following matrices: (a) 1] -2 1 0 -2 0 1 4 0 0 -5 (b) | 3 1 - -1 1 -2 (c) -2 -6 -2 1 19 5 5 -4 1.

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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6. Find the characteristic equations of the following matrices: (a) 4 0 1 -2 1 0 -2 0 1 (b) 3 0 -5 * -1 1 1 -2 (c) -2 -6 -2 1 19 5 -4 (d) -1 -1 3 -4 13 -1 50 1 1 1 0 -7 1 0 (e) (f) 5 6 2 0 -1 -8 1 0 -2 7. Find the eigenvalues of the matrices in Exercise 6. Answer: (a) 1, 2, 3 (b) -/2. 0, 2 (c) -8 (d) 2 (e) 2 (1) -4, 3 8. Find bases for the eigenspaces of the matrices in Exercise 6. 9. Find the characteristic equations of the following matrices: (a) 0 0 2 0 1 0 1 0 0 1 -2 0 0 0 0 1 (b) 10 -9 4 -2 0 -2 -7 1
Transcribed Image Text:6. Find the characteristic equations of the following matrices: (a) 4 0 1 -2 1 0 -2 0 1 (b) 3 0 -5 * -1 1 1 -2 (c) -2 -6 -2 1 19 5 -4 (d) -1 -1 3 -4 13 -1 50 1 1 1 0 -7 1 0 (e) (f) 5 6 2 0 -1 -8 1 0 -2 7. Find the eigenvalues of the matrices in Exercise 6. Answer: (a) 1, 2, 3 (b) -/2. 0, 2 (c) -8 (d) 2 (e) 2 (1) -4, 3 8. Find bases for the eigenspaces of the matrices in Exercise 6. 9. Find the characteristic equations of the following matrices: (a) 0 0 2 0 1 0 1 0 0 1 -2 0 0 0 0 1 (b) 10 -9 4 -2 0 -2 -7 1
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