Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector.11 %3D 13, х1 %3 (1, 2, —1)12 = -3, x2 = (-2, 1 0)Аз %3D —3, Xз %3D (3, 0, 1)-14-6А —45 -12-2 -43I-14-61Ах14-122132-2 -43-1-1-14-6-2-2Ax245 -121-3112x2-2 -43---14-63Ax345 -12-313x3-2-4311

Given A = -14-645-12-2-43λ1 = 13, x1 = (1, 2, -1)λ2 = -3, x2 = (-2, 1, 0)λ3 = -3, x3 = (3, 0, 1)

Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 %3D 13, х1 %3 (1, 2, —1) 12 = -3, x2 = (-2, 1 0) Аз %3D —3, Xз %3D (3, 0, 1) -1 4 -6 A = 4 5 -12 -2 -4 3 -- I -1 4 -6 1 Ах1 4 -12 2 13 2 -2 -4 3 -1 -1 -1 4 -6 -2 -2 Ax2 4 5 -12 1 -3 1 12x2 -2 -4 3 -1 4 -6 Axa 12 3

Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 %3D 13, х1 %3 (1, 2, —1) 12 = -3, x2 = (-2, 1 0) Аз %3D —3, Xз %3D (3, 0, 1) -1 4 -6 A = 4 5 -12 -2 -4 3 -- I -1 4 -6 1 Ах1 4 -12 2 13 2 -2 -4 3 -1 -1 -1 4 -6 -2 -2 Ax2 4 5 -12 1 -3 1 12x2 -2 -4 3 -1 4 -6 Axa 12 3

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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