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Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 = 6, x, = (1, 0, 0) 4 1, 1, = 4, x, = (1, 2, 0) 23 = 5, x3 = (-2, 1, 1) 6 -1 3 A =| 0 0 5 6 -1 3 1 Ax1 = 60 = 1,x1 4 1 0 5 6 -1 3 1 Ax2 = = 4 2 = 12x2 4 1 2 0 5 6 -1 3 -2 -2 Ax3 = = 5 1=13x3 4 1 0 5 1 1 1.

Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 = 6, x, = (1, 0, 0) 4 1, 1, = 4, x, = (1, 2, 0) 23 = 5, x3 = (-2, 1, 1) 6 -1 3 A =| 0 0 5 6 -1 3 1 Ax1 = 60 = 1,x1 4 1 0 5 6 -1 3 1 Ax2 = = 4 2 = 12x2 4 1 2 0 5 6 -1 3 -2 -2 Ax3 = = 5 1=13x3 4 1 0 5 1 1 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 3
 
0 4 1
0 0 5
,
?1 = 6, x1 = (1, 0, 0)

?2 = 4, x2 = (1, 2, 0)

?3 = 5, x3 = (−2, 1, 1)
Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 = 6, x, = (1, 0, 0) 12 = 4, x2 = (1, 2, 0) 13 = 5, x, = (-2, 1, 1) 6 -1 3 A = 4 1 0 5 %3D 6 -1 3 1 1 Ax1 4 1 = 6 = 1,×1 0 5 6 -1 3 1 1 Ax2 = 4 1 2 = 4 2 = 12X2 0 5 6 -1 3 -2 -2 Ax3 4 1 1= 13x3 1 = 5 0 5 1 1
Transcribed Image Text:Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 = 6, x, = (1, 0, 0) 12 = 4, x2 = (1, 2, 0) 13 = 5, x, = (-2, 1, 1) 6 -1 3 A = 4 1 0 5 %3D 6 -1 3 1 1 Ax1 4 1 = 6 = 1,×1 0 5 6 -1 3 1 1 Ax2 = 4 1 2 = 4 2 = 12X2 0 5 6 -1 3 -2 -2 Ax3 4 1 1= 13x3 1 = 5 0 5 1 1
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