Let -1 0 0 4 0 0 0 0 4 -1 0 0 -1 4 (a) Find the characteristic polynomial of A. (b) Find the dimension of the eigenspace corresponding to the largest eigenvalue.
Let -1 0 0 4 0 0 0 0 4 -1 0 0 -1 4 (a) Find the characteristic polynomial of A. (b) Find the dimension of the eigenspace corresponding to the largest eigenvalue.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 9EQ: In Exercises 7-12, show that is an eigenvector of A and find one eigenvector corresponding to this...
Question
Transcribed Image Text:#3: Let
-1
4
0
0
0
4
-1
0
0
-1
4
(a) Find the characteristic polynomial of A.
(b) Find the dimension of the eigenspace corresponding to the largest eigenvalue.
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Step 1: Write the definition of characteristics polynomial and eigenspace
VIEWStep 2: Find the required characteristic polynomial
VIEWStep 3: Find the eigenvalues of A
VIEWStep 4: Find the eigenvectors of A corresponding to the largest eigenvalue
VIEWStep 5: Find the eigenvectors
VIEWStep 6: Find the eigenspace and dimension of it
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