Verify that A; is an eigenvalue of A and that x, is a corresponding eigenvector. 21=5, x1 = (1, 2, -1) 22 -3, x2 (-2, 1 0) 13=-3, x3 = (3, 0, 1) -2 2-3 A = 2. 1-6 %D %3D -1-2 0

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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Question 5
Verify that A; is an eigenvalue of A and that x, is a corresponding eigenvector.
d1=5, x1 (1, 2, -1)
12=-3, x2 (-2, 1 0)
d3=-3, x3 (3, 0, 1)
-2
2 -3
A =
2.
1-6
-1 -2 0]
Ax1 =
2.
5.
= 1,x1
-2
2 -3
Ax2 =
2
1 -6
12x2
-1 -2
-2
2 -3
Ax3 =
2 1-6
-30
= A3x3
-1 -2 0][ 1
Transcribed Image Text:Verify that A; is an eigenvalue of A and that x, is a corresponding eigenvector. d1=5, x1 (1, 2, -1) 12=-3, x2 (-2, 1 0) d3=-3, x3 (3, 0, 1) -2 2 -3 A = 2. 1-6 -1 -2 0] Ax1 = 2. 5. = 1,x1 -2 2 -3 Ax2 = 2 1 -6 12x2 -1 -2 -2 2 -3 Ax3 = 2 1-6 -30 = A3x3 -1 -2 0][ 1
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