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
11 please step by step and write cl
![4. Use this information to diagonalize A.
with eigenvalues 5, 3, and -2, and suppose you know that
= 3 is two-dimensional. Do you have enough information to
x
nalizable?
VI
6
5.
6.
2 2
13
1
1
1
1
426
0
-2
0
1
17
1
2
2:
1
2
0 -1
-1
0
0-2
5
0
=
5 0
IL:
2
1
0
0 0
=
4
5]
0 -15
1
I
0
0
0
0
5
0
0
1
0 0
1/4]
1/4 1/2
1/4 1/2 -3/4
1/4 -1/2 1/4]
E
eru
0
0
0
4
2
][/
-1
01
0
10
1 4
0-2
0
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%2Fef7e726a-0ea0-421a-8dc8-9d10a38e345b%2F9lhncy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Use this information to diagonalize A.
with eigenvalues 5, 3, and -2, and suppose you know that
= 3 is two-dimensional. Do you have enough information to
x
nalizable?
VI
6
5.
6.
2 2
13
1
1
1
1
426
0
-2
0
1
17
1
2
2:
1
2
0 -1
-1
0
0-2
5
0
=
5 0
IL:
2
1
0
0 0
=
4
5]
0 -15
1
I
0
0
0
0
5
0
0
1
0 0
1/4]
1/4 1/2
1/4 1/2 -3/4
1/4 -1/2 1/4]
E
eru
0
0
0
4
2
][/
-1
01
0
10
1 4
0-2
0
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).
![4. Use this information to diagonalize A.
with eigenvalues 5, 3, and -2, and suppose you know that
= 3 is two-dimensional. Do you have enough information to
x
nalizable?
VI
6
5.
6.
2 2
13
1
1
1
1
426
0
-2
0
1
17
1
2
2:
1
2
0 -1
-1
0
0-2
5
0
=
5 0
IL:
2
1
0
0 0
=
4
5]
0 -15
1
I
0
0
0
0
5
0
0
1
0 0
1/4]
1/4 1/2
1/4 1/2 -3/4
1/4 -1/2 1/4]
E
eru
0
0
0
4
2
][/
-1
01
0
10
1 4
0-2
0
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%2Fef7e726a-0ea0-421a-8dc8-9d10a38e345b%2Fba70dl7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Use this information to diagonalize A.
with eigenvalues 5, 3, and -2, and suppose you know that
= 3 is two-dimensional. Do you have enough information to
x
nalizable?
VI
6
5.
6.
2 2
13
1
1
1
1
426
0
-2
0
1
17
1
2
2:
1
2
0 -1
-1
0
0-2
5
0
=
5 0
IL:
2
1
0
0 0
=
4
5]
0 -15
1
I
0
0
0
0
5
0
0
1
0 0
1/4]
1/4 1/2
1/4 1/2 -3/4
1/4 -1/2 1/4]
E
eru
0
0
0
4
2
][/
-1
01
0
10
1 4
0-2
0
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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