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7 -1 6 -5 -5 Ax3 = 5 1 1 = 6 1 = 13X3 %3D 0 6 1 1

7 -1 6 -5 -5 Ax3 = 5 1 1 = 6 1 = 13X3 %3D 0 6 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 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 1, %3D 7, х, %3D (1, 0, 0) 12 = 5, x2 = (1, 2, 0) 13 = 6, x3 = (-5, 1, 1) 7 -1 6 A = 5 1 0 6 7 -1 6 1 1 Ax, = 5 1 7 0 6 7 -1 6 1 1 Ax2 5 1 2 = 5 2 = 12x2 %3D %3D 0 6 7 -1 6 -5 -5 Ax3 = 5 1 = 6 = 13X3 1 1 0 6 1 1
Transcribed Image Text:Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 1, %3D 7, х, %3D (1, 0, 0) 12 = 5, x2 = (1, 2, 0) 13 = 6, x3 = (-5, 1, 1) 7 -1 6 A = 5 1 0 6 7 -1 6 1 1 Ax, = 5 1 7 0 6 7 -1 6 1 1 Ax2 5 1 2 = 5 2 = 12x2 %3D %3D 0 6 7 -1 6 -5 -5 Ax3 = 5 1 = 6 = 13X3 1 1 0 6 1 1
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