For each eigenvalue of A, find an associ Find a diagonal matrix D and an inver 0 1 0 1.1 0 0 01 0. 0 2 0 9.1 0 1 020 0 1 0 040 5. 0 0 1 (:D) (:) 46. 0 0 1 01 0 01 0 01 101 10. 42. 1 7.1 1 1 50. 0 1 0 100 020 01 0 103 010 3 2 2 54. 2 3 2 2 2 3 58. 0 1 (ii) 1 -1 1 43 47 51 55 59
For each eigenvalue of A, find an associ Find a diagonal matrix D and an inver 0 1 0 1.1 0 0 01 0. 0 2 0 9.1 0 1 020 0 1 0 040 5. 0 0 1 (:D) (:) 46. 0 0 1 01 0 01 0 01 101 10. 42. 1 7.1 1 1 50. 0 1 0 100 020 01 0 103 010 3 2 2 54. 2 3 2 2 2 3 58. 0 1 (ii) 1 -1 1 43 47 51 55 59
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
Q48 please
Transcribed Image Text:Problem III Let A denote the matrix given below.
(i) Find all eigenvalues of the matrix A.
(ii) For each eigenvalue of A, find an associated eigenvector.
(iii) Find a diagonal matrix D and an invertible matrix U such that A = UDU-¹.
0 1 0
1 0
2 0
4
41.
-(:D) - (:D) * () +(:)
1 00
42.
100
43. 200
100
0 10
020
0 1
45. 0 0 1
01 0
53.
57.
46.
0 1 1
10 1
1 10
04
001
010
0
01
020
49.
.. (1) 50 (1) 4(:¦:-) (9)
0
103
51. 2 0 -1
52.
401
2
01 0
010,
-1
47. 0 02
20
0
32 2
54. 232
223
55.
48.
110
0 1
0 1 1
010
004
0 1 0
56.
1
1
1 -2 1
-2 1
01 0
0 1 0
01 0
0 50
(D)(-+) (9) -(-5)
1 1 1
58. 1 -1 1
59. 5 1 1
60. 1
-1 1
0 1 0
0 10
01 0
0
10
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