Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 41EQ
Related questions
Question
17 pl
![, and v₂
fA. Use this information to diagonalize A.
rix with eigenvalues 5, 3, and -2, and suppose you know that
= 3 is two-dimensional. Do you have enough information
gonalizable?
V₁ =
5.
6.
2 2 17
1
1
1
1
1
4
2
0
-2
0
1
232
1
2_
-1
1 2
0 -1
5
+][
0
H
0-2
5
4
05
0 00
0
1
0 -171
1
2
0
0
1
05
5
0 0
96
011/4
0 1/4
5 00
1/2 1/47
1/2-3/4
[1/4-1/2 1/4_
0
I
4
0
2
to
-1
ei einer
0 17
1 4
0-2
Diagonalize the matrices in Exercises 7-20, if possible. The
eigenvalues for Exercises 11-16 are as follows: (11) λ = 1,2,3;
(12) λ = 2,8; (13) λ = 5, 1; (14) λ = 5, 4; (15) λ = 3,1; (16)
λ = 2, 1. For Exercise 18, one eigenvalue is λ = 5 and one
eigenvector is (-2, 1, 2).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22b1319c-242c-4915-8f56-7c035e43f773%2F819be859-f1b7-40ce-b9d6-5b7774f55253%2Fraz3nxw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:, and v₂
fA. Use this information to diagonalize A.
rix with eigenvalues 5, 3, and -2, and suppose you know that
= 3 is two-dimensional. Do you have enough information
gonalizable?
V₁ =
5.
6.
2 2 17
1
1
1
1
1
4
2
0
-2
0
1
232
1
2_
-1
1 2
0 -1
5
+][
0
H
0-2
5
4
05
0 00
0
1
0 -171
1
2
0
0
1
05
5
0 0
96
011/4
0 1/4
5 00
1/2 1/47
1/2-3/4
[1/4-1/2 1/4_
0
I
4
0
2
to
-1
ei einer
0 17
1 4
0-2
Diagonalize the matrices in Exercises 7-20, if possible. The
eigenvalues for Exercises 11-16 are as follows: (11) λ = 1,2,3;
(12) λ = 2,8; (13) λ = 5, 1; (14) λ = 5, 4; (15) λ = 3,1; (16)
λ = 2, 1. For Exercise 18, one eigenvalue is λ = 5 and one
eigenvector is (-2, 1, 2).
![, and v₂
fA. Use this information to diagonalize A.
rix with eigenvalues 5, 3, and -2, and suppose you know that
= 3 is two-dimensional. Do you have enough information
gonalizable?
V₁ =
5.
6.
2 2 17
1
1
1
1
1
4
2
0
-2
0
1
232
1
2_
-1
1 2
0 -1
5
+][
0
H
0-2
5
4
05
0 00
0
1
0 -171
1
2
0
0
1
05
5
0 0
96
011/4
0 1/4
5 00
1/2 1/47
1/2-3/4
[1/4-1/2 1/4_
0
I
4
0
2
to
-1
ei einer
0 17
1 4
0-2
Diagonalize the matrices in Exercises 7-20, if possible. The
eigenvalues for Exercises 11-16 are as follows: (11) λ = 1,2,3;
(12) λ = 2,8; (13) λ = 5, 1; (14) λ = 5, 4; (15) λ = 3,1; (16)
λ = 2, 1. For Exercise 18, one eigenvalue is λ = 5 and one
eigenvector is (-2, 1, 2).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22b1319c-242c-4915-8f56-7c035e43f773%2F819be859-f1b7-40ce-b9d6-5b7774f55253%2Fjwnrujk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:, and v₂
fA. Use this information to diagonalize A.
rix with eigenvalues 5, 3, and -2, and suppose you know that
= 3 is two-dimensional. Do you have enough information
gonalizable?
V₁ =
5.
6.
2 2 17
1
1
1
1
1
4
2
0
-2
0
1
232
1
2_
-1
1 2
0 -1
5
+][
0
H
0-2
5
4
05
0 00
0
1
0 -171
1
2
0
0
1
05
5
0 0
96
011/4
0 1/4
5 00
1/2 1/47
1/2-3/4
[1/4-1/2 1/4_
0
I
4
0
2
to
-1
ei einer
0 17
1 4
0-2
Diagonalize the matrices in Exercises 7-20, if possible. The
eigenvalues for Exercises 11-16 are as follows: (11) λ = 1,2,3;
(12) λ = 2,8; (13) λ = 5, 1; (14) λ = 5, 4; (15) λ = 3,1; (16)
λ = 2, 1. For Exercise 18, one eigenvalue is λ = 5 and one
eigenvector is (-2, 1, 2).
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