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. 41. 0 1 0 100 0 10 42. 0 1 0 100 020 0 2 0 43. 200 0 1 0 44. 0 4 0 100 0 1 0
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. 41. 0 1 0 100 0 10 42. 0 1 0 100 020 0 2 0 43. 200 0 1 0 44. 0 4 0 100 0 1 0
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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Please solve parts 41-44 of this problem... take as much time as necessary... this is for
![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
0
2 0
4(:D) 2 (1:5) + (1) 4(:)
41.
1 00
42.
100
43. 200
100
0 10
020
010
0 1
45. 001
01 0
53.
57.
46.
0 1 1
101
1 10
04
001
010
0
01
020
49.
.. (1) 50 (1) 44(:¦:-) (9)
0
03
51. 20-1
52.
401
20
0
01 0
0 1
0
54.
-1
47. 0 02
0 20
32 2
232
223
55.
48.
1 1 0
0 1
0 1 1
01 0
004
0 1 0
56.
1 1
1 -2 1
-2 1
01 0
0 1 0
01 0
0 50
(D)(-+) (9) - (-)
1 1 1
58. 1 -1 1
59. 5 1 1
60. 1 -1 1
0 1 0
0 10
01 0
0 10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47d370c3-9e4b-442d-9a89-d591c5ced338%2F03f8648f-8b5e-42d0-b3b2-eac82340e41b%2Fbvu5tkm_processed.png&w=3840&q=75)
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
0
2 0
4(:D) 2 (1:5) + (1) 4(:)
41.
1 00
42.
100
43. 200
100
0 10
020
010
0 1
45. 001
01 0
53.
57.
46.
0 1 1
101
1 10
04
001
010
0
01
020
49.
.. (1) 50 (1) 44(:¦:-) (9)
0
03
51. 20-1
52.
401
20
0
01 0
0 1
0
54.
-1
47. 0 02
0 20
32 2
232
223
55.
48.
1 1 0
0 1
0 1 1
01 0
004
0 1 0
56.
1 1
1 -2 1
-2 1
01 0
0 1 0
01 0
0 50
(D)(-+) (9) - (-)
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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