Problem III Let B denote the matrix given below. (i) Find all eigenvalues of the matrix B. (ii) For each eigenvalue of B, find an associated eigenvector. (iii) Is the matrix B diagonalizable? Explain. (iv) Find all eigenvalues of the matrix 2B +31, where I is the identity matrix. 41. 101 01 01 42. 1 0 1 03 101 43. 1 0 1 0 -1 01 44. -2
Problem III Let B denote the matrix given below. (i) Find all eigenvalues of the matrix B. (ii) For each eigenvalue of B, find an associated eigenvector. (iii) Is the matrix B diagonalizable? Explain. (iv) Find all eigenvalues of the matrix 2B +31, where I is the identity matrix. 41. 101 01 01 42. 1 0 1 03 101 43. 1 0 1 0 -1 01 44. -2
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
Parts 41-44 Please
![Problem III Let B denote the matrix given below.
(i) Find all eigenvalues of the matrix B.
(ii) For each eigenvalue of B, find an associated eigenvector.
(iii) Is the matrix B diagonalizable? Explain.
(iv) Find all eigenvalues of the matrix 2B + 31, where I is the identity matrix.
10 1
4¹. (; ; ;)
0 1 0
1
1
0
45.- (1 - 1)
0 -3
01
49.
53.
57.
00
30 1
0
0 1 0
1
2
000
201
030
102
42.
46.
50.
54.
58.
1 0 1
030
1 0 1
10 1
020
10 1
00
02
020
02
20-1
0
(₁
20
02
0
:)
0
-1 0
-1
0
43.
47.
51.
55.
59.
1 01
0
1 0
000
101
01 0
00
302
020
-1 0
02
10
20 -2
2
-1 1
10
-1
44.
48.
52.
56.
60.
1
0
1
000
201
0 1 0
0 1
1
0
000
(
0
-2 0
01
10 -1
02
0
1
0
2 -1
0
-2
1
0
2 -1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b19493d-2e0b-4edb-977e-29215d3bb0dd%2Fa5bc05d9-8006-4cbe-a266-4afc575f2dea%2Fjaoehhg_processed.png&w=3840&q=75)
Transcribed Image Text:Problem III Let B denote the matrix given below.
(i) Find all eigenvalues of the matrix B.
(ii) For each eigenvalue of B, find an associated eigenvector.
(iii) Is the matrix B diagonalizable? Explain.
(iv) Find all eigenvalues of the matrix 2B + 31, where I is the identity matrix.
10 1
4¹. (; ; ;)
0 1 0
1
1
0
45.- (1 - 1)
0 -3
01
49.
53.
57.
00
30 1
0
0 1 0
1
2
000
201
030
102
42.
46.
50.
54.
58.
1 0 1
030
1 0 1
10 1
020
10 1
00
02
020
02
20-1
0
(₁
20
02
0
:)
0
-1 0
-1
0
43.
47.
51.
55.
59.
1 01
0
1 0
000
101
01 0
00
302
020
-1 0
02
10
20 -2
2
-1 1
10
-1
44.
48.
52.
56.
60.
1
0
1
000
201
0 1 0
0 1
1
0
000
(
0
-2 0
01
10 -1
02
0
1
0
2 -1
0
-2
1
0
2 -1
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