Matrix A is factored in the form PDP1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 30 - 12 -4 0 -1 0 0 1 A= 6 6 24 1 0 6 0 2 1 8 = 0 0 6 1 0 0 0 0 3 -10 -4 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 basis for the corresponding eigenspace is { OB. In ascending order, the two distinct eigenvalues are a, =| Bases for the corresponding eigenspaces are { and iz = and respectively. O C. In ascending order, the three distinct eigenvalues are 4 = and a = Bases for the corresponding eigenspaces are and respectively. %3D

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Matrix A is factored in the form PDP1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.
30 - 12
-40 -1
6 00
0 0 1
A= 6 6 24
0 1 2
0 6 0
2 1
8
0 0
1
0 03
-10 -4
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 { }
O B. In ascending order, the two distinct eigenvalues are , =
and , =
Bases for the corresponding eigenspaces are } and { }, respectively.
OC.
In ascending order, the three distinct eigenvalues are , =
and =
Bases for the corresponding eigenspaces are { }, { }, and { }, respectively.
Transcribed Image Text:Matrix A is factored in the form PDP1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 30 - 12 -40 -1 6 00 0 0 1 A= 6 6 24 0 1 2 0 6 0 2 1 8 0 0 1 0 03 -10 -4 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 { } O B. In ascending order, the two distinct eigenvalues are , = and , = Bases for the corresponding eigenspaces are } and { }, respectively. OC. In ascending order, the three distinct eigenvalues are , = and = Bases for the corresponding eigenspaces are { }, { }, and { }, respectively.
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