Matrix A is factored in the form PDP. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. A= 122 2 500 010 001 1 0-1 1-1 0 1 1 -12 114 314 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) OA. There is one distinct eigenvalue, XA basis for the corresponding eigenspace is OB. In ascending order, the two distinct eigenvalues are X, and A OC. In ascending order, the three distinct eigenvalues - and X- GELED Bases for the corresponding eigenspaces are and respectively Bases for the corresponding eigenspaces are, and respectively

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 24EQ
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Matrix A is factored in the form PDP. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.
1
21
A= 31
122
1 1 2
1 0-1
1-1 0
500
010
001
4
Select the correct choice below and fill in the answer boxes to complete your choice.
(Use a comma to separate vectors as needed.)
OA. There is one distinct eigenvalue, X= A basis for the corresponding eigenspace is
OB. In ascending order, the two distinct eigenvalues are A
OC. In ascending order, the three distinct eigenvalues are
and
GELES
Bases for the corresponding eigenspaces are and
Bases for the corresponding eigenspaces are y
and
respectively
..and respectively
Transcribed Image Text:↑ Matrix A is factored in the form PDP. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 1 21 A= 31 122 1 1 2 1 0-1 1-1 0 500 010 001 4 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) OA. There is one distinct eigenvalue, X= A basis for the corresponding eigenspace is OB. In ascending order, the two distinct eigenvalues are A OC. In ascending order, the three distinct eigenvalues are and GELES Bases for the corresponding eigenspaces are and Bases for the corresponding eigenspaces are y and respectively ..and respectively
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