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Verify that A, is an eigenvalue of A and that x, is a corresponding eigenvector. 2 = 6, x, = (1, 0, 0) 12 = 4, x2 = (1, 2, 0) 23 = 5, x3 = (-3, 1, 1) 6. -1 4 %3! %3D A = 4 1 %3D 0 5 6 -1 4 Ax, = 4 1 = 1,x1 0 5 6 -1 4 Ax2 = 2 = 1,x2 4 1 2 0 5 6 -1 4 -3 Ax3 = 1 = 13x3 4 1 = 5 0 5 1

Verify that A, is an eigenvalue of A and that x, is a corresponding eigenvector. 2 = 6, x, = (1, 0, 0) 12 = 4, x2 = (1, 2, 0) 23 = 5, x3 = (-3, 1, 1) 6. -1 4 %3! %3D A = 4 1 %3D 0 5 6 -1 4 Ax, = 4 1 = 1,x1 0 5 6 -1 4 Ax2 = 2 = 1,x2 4 1 2 0 5 6 -1 4 -3 Ax3 = 1 = 13x3 4 1 = 5 0 5 1

Linear Algebra: A Modern Introduction
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 5EQ: In Exercises 1-6, show that vis an eigenvector of A and find the corresponding eigenvalue....
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Verify that ?i is an eigenvalue of A and that xi is a corresponding eigenvector.

A = 
 
6 −1 4
 
0 4 1
0 0 5
,
?1 = 6, x1 = (1, 0, 0)

?2 = 4, x2 = (1, 2, 0)

?3 = 5, x3 = (−3, 1, 1)
Ax1



 =
 
6 −1 4
 
0 4 1
0 0 5
 
1
 
0
0



=
       
     
     
 
=
6
 
1
 
0
0



=
?1x1
Ax2



 =
 
6 −1 4
 
0 4 1
0 0 5
 
1
 
2
0



=
       
     
     
 
=
4
 
1
 
2
0



=
?2x2
Ax3



 =
 
6 −1 4
 
0 4 1
0 0 5
 
−3
 
1
1



=
       
     
     
 
=
5
 
−3
 
1
1



=
?3x3
Verify that A, is an eigenvalue of A and that x, is a corresponding eigenvector. 21 = 6, x, = (1, 0, 0) 12 = 4, x, = (1, 2, 0) 23 = 5, x3 = (-3, 1, 1) 6 -1 4 A = 4 1 %3D 0 5 %3D 6 -1 4 4 1 = 6 0 = 1,x1 %3D 0 5 6 -1 4 Ax2 = = 1,x2 4 1 2 0 5 6 -1 4 -3 -3 Ax3 = 1 = 13x3 4 1 1 = 5 0 5 1
Transcribed Image Text:Verify that A, is an eigenvalue of A and that x, is a corresponding eigenvector. 21 = 6, x, = (1, 0, 0) 12 = 4, x, = (1, 2, 0) 23 = 5, x3 = (-3, 1, 1) 6 -1 4 A = 4 1 %3D 0 5 %3D 6 -1 4 4 1 = 6 0 = 1,x1 %3D 0 5 6 -1 4 Ax2 = = 1,x2 4 1 2 0 5 6 -1 4 -3 -3 Ax3 = 1 = 13x3 4 1 1 = 5 0 5 1
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