Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. = 13, x, = (1, 2, –1) h2 = -3, x, = (-2, 1 0) 23 = -3, x3 = (3, 0, 1) -1 4 -6 A = 4 5 -12 -2 -4 3 -1 4 -6 1 Ах, 5 -12 2 = 1,x1 4 2 13 -2 -4 -1 -1 4 -6 Ax2 = = -3 1 = 1,x2 4 5 -12 -2 -4 -1 4 -6 3. 3 Ax3 = -3 0 = 13x3 4 5 -12 = -2 -4 1.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector.
= 13, x, = (1, 2, -1)
12 = -3, x2 = (-2, 1 0)
з 3 -3, х3 3 (3, 0, 1)
-1
4
-6
A =
4
5 -12
-2 -4
3
-1
4
-6
1.
Ax1 =
2 = 1,x1
4
5 -12
= 13
-2 -4
3
-1
-1
4
-6
-2
Ax2 =
1= 1,x2
4
5 -12
1
-3
-2 -4
3
-1
4
-6
3
Ax3 =
= -3
= 13X3
4
5 -12
-2 -4
3
1.
1.
Transcribed Image Text:Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. = 13, x, = (1, 2, -1) 12 = -3, x2 = (-2, 1 0) з 3 -3, х3 3 (3, 0, 1) -1 4 -6 A = 4 5 -12 -2 -4 3 -1 4 -6 1. Ax1 = 2 = 1,x1 4 5 -12 = 13 -2 -4 3 -1 -1 4 -6 -2 Ax2 = 1= 1,x2 4 5 -12 1 -3 -2 -4 3 -1 4 -6 3 Ax3 = = -3 = 13X3 4 5 -12 -2 -4 3 1. 1.
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