Verify that A, is an eigenvalue of A and that x, is a corresponding eigenvector. 2, = 8, x (1, 0, 0) 12 = 6, x, = (1, 2, 0) dg = 7, x3 = (-5, 1, 1) 8 -1 6 A = 6 1 0 7 8 -1 6 Ax, = 6 1 80 = 1,x1 0 7 8 -1 6 6 1 0 7 Ax2 = = 6| 2 = 12x2 2 8 -1 6 -5 -5 Ax3 = 1 = 13x3 6 1 1 0 7 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
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Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector.
1 = 8, x, = (1, 0, 0)
12 = 6, x, = (1, 2, 0)
23 = 7, x3 = (-5, 1, 1)
8 -1 6
A =
6 1
0 7
8 -1 6
1
Ax, =
6 1
= 8 0
0 7
8 -1 6
1
Ax2 =
6 1
= 6 2
0 7
8 -1 6
-5
5
Ax3 =
6 1
1 = 13x3
1
= /
0 7
1
1
Transcribed Image Text:Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. 1 = 8, x, = (1, 0, 0) 12 = 6, x, = (1, 2, 0) 23 = 7, x3 = (-5, 1, 1) 8 -1 6 A = 6 1 0 7 8 -1 6 1 Ax, = 6 1 = 8 0 0 7 8 -1 6 1 Ax2 = 6 1 = 6 2 0 7 8 -1 6 -5 5 Ax3 = 6 1 1 = 13x3 1 = / 0 7 1 1
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