Verify that 2, is an eigenvalue of A and that x; is a corresponding eigenvector. 11 = 8, x1 = (1, 0, 0) 12 = 6, x2 = (1, 2, 0) 13 = 7, x3 = (-1, 1, 1) 8 -1 2 A = 6 1 0 7 8 -1 2 Ax1 = 6 1 0 7 8 -1 2 Ax2 = 6 1 6 2 0 7 8 -1 2 Ax3 = 6 1 1 = 7 1 13x3 0 7 1 1

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 4EQ: In Exercises 1-6, show that vis an eigenvector of A and find the corresponding eigenvalue....
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Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector.
11 = 8, x1 = (1, 0, 0)
12 = 6, x2 = (1, 2, 0)
13 = 7, x3 = (-1, 1, 1)
8 -1 2
A =
6 1
0 7
8 -1 2
1
Ax1 =
6 1
0 7
8 -1 2
Ax, =
6 1
6 2
0 7
8 -1 2
Ax3 =
6 1
= 7
= 13x3
1
1
=
0 7
1
Transcribed Image Text:Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 = 8, x1 = (1, 0, 0) 12 = 6, x2 = (1, 2, 0) 13 = 7, x3 = (-1, 1, 1) 8 -1 2 A = 6 1 0 7 8 -1 2 1 Ax1 = 6 1 0 7 8 -1 2 Ax, = 6 1 6 2 0 7 8 -1 2 Ax3 = 6 1 = 7 = 13x3 1 1 = 0 7 1
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