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. 3 0 -2 - 1 0 - 1 5 0 0 0 0 1 A = 6 5 6 0 1 3 0 50 3 1 3 = 0 0 5 0 0 3 -1 0 - 1 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) A. There is one distinct eigenvalue, A = A basis for the corresponding eigenspace is B. In ascending order, the two distinct eigenvalues are = and 2 = Bases for the corresponding eigenspaces are O and {}, respectively. O C. In ascending order, the three distinct eigenvalues are ng = and 3 = 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. 3 0 -2 - 1 0 - 1 5 0 0 0 0 1 A = 6 5 6 0 1 3 0 50 3 1 3 = 0 0 5 0 0 3 -1 0 - 1 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) A. There is one distinct eigenvalue, A = A basis for the corresponding eigenspace is B. In ascending order, the two distinct eigenvalues are = and 2 = Bases for the corresponding eigenspaces are O and {}, respectively. O C. In ascending order, the three distinct eigenvalues are ng = and 3 = 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.
3 0
2
-1 0
- 1
5 0 0
1
-
A =
6 5
6.
1
3
050
3
1
3
0 0
1
0 0 3
-1 0
- 1
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, A =. A basis for the corresponding eigenspace is { }.
B. In ascending order, the two distinct eigenvalues are , =
and 12 =
Bases for the corresponding eigenspaces are {
and {
, respectively.
%3D
C. In ascending order, the three distinct eigenvalues are , =, 12 =
and A3 =
Bases for the corresponding eigenspaces are
{0{}, and {},
respectively.
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