erify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. [7 -1 9] A = 0 5 1 22 = 5, x2 = (1, 2, 0) 0 0 6] 11 = 7, x1 = (1, 0, 0) 23 = 6, x3 = (-8, 1, 1) 7 -1 9 0 5 1 0 0 6 4x1 7 -1 9 0 5 1| 2 0 06, Ax2 5 2 = 12x2 = 7 -1 9 -8 -8 4x3 - 13X3 5 1 = 6. 0 6 H O O

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 A, is an eigenvalue of A and that x; is a corresponding eigenvector.
7 -1 9
5 1
21 = 7, x1 = (1, 0, 0)
22 = 5, x2 - (1, 2, 0)
23 = 6, x3 = (-8, 1, 1)
A =
%3D
0 6
7 -1 9
1.
Ax, =
5 1
7
=
0 6
7 -1 9
-
Ax2
5 1
5 2
=
=
0 6
7 -1 9
5 1
-8
-8
Ax3
=
= 6
1
0 6
Transcribed Image Text:Verify that A, is an eigenvalue of A and that x; is a corresponding eigenvector. 7 -1 9 5 1 21 = 7, x1 = (1, 0, 0) 22 = 5, x2 - (1, 2, 0) 23 = 6, x3 = (-8, 1, 1) A = %3D 0 6 7 -1 9 1. Ax, = 5 1 7 = 0 6 7 -1 9 - Ax2 5 1 5 2 = = 0 6 7 -1 9 5 1 -8 -8 Ax3 = = 6 1 0 6
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