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Verify that 1, is an eigenvalue of A and that x, is a corresponding eigenvector. 2 = -11, x, = (1, 2, -1) 6, 12 = -3, x2 = (-2, 1 0) 23 = -3, x, = (3, 0, 1) -4 -2 3 A = -2 -7 %3D 1 2 -6 %3D -4 -2 Ax1 -2 -7 6 -11 %3D 1 2 -6 -1 -4 -2 3 -2 2 Ax, = -3 1 =12x2 -2 -7 6 1 2 -6 -4 -2 3 Ax3 = -2 -7 -3 0 = 13x3 %3D 1 2 -6

Verify that 1, is an eigenvalue of A and that x, is a corresponding eigenvector. 2 = -11, x, = (1, 2, -1) 6, 12 = -3, x2 = (-2, 1 0) 23 = -3, x, = (3, 0, 1) -4 -2 3 A = -2 -7 %3D 1 2 -6 %3D -4 -2 Ax1 -2 -7 6 -11 %3D 1 2 -6 -1 -4 -2 3 -2 2 Ax, = -3 1 =12x2 -2 -7 6 1 2 -6 -4 -2 3 Ax3 = -2 -7 -3 0 = 13x3 %3D 1 2 -6

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. 2= -11, x, = (1, 2, -1) 6, 22 = -3, x2 = (-2, 1 0) 23 = -3, x, (3, 0, 1) -4 -2 %3D A =-2 -7 %3D %3D 1 2 -6 %3D %3D -4 -2 Ax1 2 =1,x1 %3D -2 -7 6 --11 1 2 -6 -4 -2 -2 -2 Ax2 = -2 -7 6. 1 -3 1 1 2 -6 -4 -2 3 Ax3 = -2 -7 -3 0 = 13x3 1 2 -6
Transcribed Image Text:Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. 2= -11, x, = (1, 2, -1) 6, 22 = -3, x2 = (-2, 1 0) 23 = -3, x, (3, 0, 1) -4 -2 %3D A =-2 -7 %3D %3D 1 2 -6 %3D %3D -4 -2 Ax1 2 =1,x1 %3D -2 -7 6 --11 1 2 -6 -4 -2 -2 -2 Ax2 = -2 -7 6. 1 -3 1 1 2 -6 -4 -2 3 Ax3 = -2 -7 -3 0 = 13x3 1 2 -6
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