A diagonalization of the matrix A is given in the form P-¹AP = D. List the eigenvalues of A and bases for the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) ^₂ = ch 516076 0 0 501 1 1 has eigenspace 0 has eigenspace 0 000 (LF) 40) span span (smallest λ-value) -UT has eigenspace span (largest λ-value)
A diagonalization of the matrix A is given in the form P-¹AP = D. List the eigenvalues of A and bases for the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) ^₂ = ch 516076 0 0 501 1 1 has eigenspace 0 has eigenspace 0 000 (LF) 40) span span (smallest λ-value) -UT has eigenspace span (largest λ-value)
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
![A diagonalization of the matrix A is given in the form P-¹AP = D. List the eigenvalues of A and bases for the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the
same eigenspaces.)
d₁ =
^₂ =
^3 =
5
6
0
1
6
1
H6OL6
1
6 6
1 0
6
1 1
5 1 1
0 1 0
501
1 0-1
0-1 0
1 1
5
has eigenspace span
has eigenspace span
600
0 1 0
]-[88]
=
000
has eigenspace span
↓ 1
→
(smallest λ-value)
(largest λ-value)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67ad69fc-d7b2-4082-8b18-7ae4b62544b8%2Fbc8038ab-ab0b-407d-b56e-f092ccaff1e9%2Fxh1ox9b_processed.png&w=3840&q=75)
Transcribed Image Text:A diagonalization of the matrix A is given in the form P-¹AP = D. List the eigenvalues of A and bases for the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the
same eigenspaces.)
d₁ =
^₂ =
^3 =
5
6
0
1
6
1
H6OL6
1
6 6
1 0
6
1 1
5 1 1
0 1 0
501
1 0-1
0-1 0
1 1
5
has eigenspace span
has eigenspace span
600
0 1 0
]-[88]
=
000
has eigenspace span
↓ 1
→
(smallest λ-value)
(largest λ-value)
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