Verify that 1, is an eigenvalue of A and that x, is a corresponding eigenvector. 9 -1 2 2, = 9, x, = (1, 0, 0) A = 7 1 1 12 = 7, x2 = (1, 2, 0) %3D 0 8 Лз 3D 8, х3 %3D (-1, 1, 1) 9 -1 2 7 1 1 Ax, = = 9 0 = 1,x1 0 8 9 -1 2 1 1 Ax2 = 7 1 2 = 7 2 = 12X2 %3D %3D 0 8 9 -1 2 1 Ax3 = 7 1 = 8 1= 13x3 %3D 0 8 1 1

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.5: Iterative Methods For Computing Eigenvalues
Problem 46EQ
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Verify that 1, is an eigenvalue of A and that x, is a corresponding eigenvector.
11 = 9, x, = (1, 0, 0)
| 12 = 7, x2 = (1, 2, 0)
0 8] 13 = 8, x3 = (-1, 1, 1)
9 -1 2
A =
7 1
9 -1 2
1
1
Ax1 :
7 1
= 9 0
0 8
9 -1 2
1
1
Ax, =
7 1
2
= 7 2
0 8
9 -1 2
-1
-1
Ax3 :
7 1
= 8
1=13x3
1
%3D
0 8
1
1
Transcribed Image Text:Verify that 1, is an eigenvalue of A and that x, is a corresponding eigenvector. 11 = 9, x, = (1, 0, 0) | 12 = 7, x2 = (1, 2, 0) 0 8] 13 = 8, x3 = (-1, 1, 1) 9 -1 2 A = 7 1 9 -1 2 1 1 Ax1 : 7 1 = 9 0 0 8 9 -1 2 1 1 Ax, = 7 1 2 = 7 2 0 8 9 -1 2 -1 -1 Ax3 : 7 1 = 8 1=13x3 1 %3D 0 8 1 1
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