Matrix A is factored in the form PDP-1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 1 6 211 2 1 2 A = 1 2 1 = 2 0-2 112 400 010 21 0 001 1 - 16 m 6 1 1 3 3 1 6 1 6 2 3 1 1 3 6 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) O A. There is one distinct eigenvalue, λ = A basis for the corresponding eigenspace is {}. OB. In ascending order, the two distinct eigenvalues are λ₁ = OC. In ascending order, the three distinct eigenvalues are >₁= and 2₂ = Bases for the corresponding eigenspaces are {}and {}, respectively. ₁^₂=₁ and 23 = . Bases for the corresponding eigenspaces are {}, {}, and {}, respectively.
Matrix A is factored in the form PDP-1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 1 6 211 2 1 2 A = 1 2 1 = 2 0-2 112 400 010 21 0 001 1 - 16 m 6 1 1 3 3 1 6 1 6 2 3 1 1 3 6 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) O A. There is one distinct eigenvalue, λ = A basis for the corresponding eigenspace is {}. OB. In ascending order, the two distinct eigenvalues are λ₁ = OC. In ascending order, the three distinct eigenvalues are >₁= and 2₂ = Bases for the corresponding eigenspaces are {}and {}, respectively. ₁^₂=₁ and 23 = . Bases for the corresponding eigenspaces are {}, {}, and {}, respectively.
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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Transcribed Image Text:Matrix A is factored in the form PDP-1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.
2 1 1
A = 1 2 1
112
1 2
400
2
= 2 0-2 0 10
2-1 0 001
- 16
- 16 -|m
-182/3
1 1
1
ح اس
3 3
1
6
6
1 1
3
-6
Select the correct choice below and fill in the answer boxes to complete your choice.
(Use a comma to separate vectors as needed.)
O A. There is one distinct eigenvalue, λ = . A basis for the corresponding eigenspace is {}.
=
O B. In ascending order, the two distinct eigenvalues are ₁ and 2₂ =
OC. In ascending order, the three distinct eigenvalues are ₁ = ₂ = ₁ and 23 = |
22
Bases for the corresponding eigenspaces are {and {}, respectively.
Bases for the corresponding eigenspaces are {}, {}, and {}, respectively.
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