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AX1 AX2 -4-2 3 1 СЕВЕ -2-7 6 2 1 2 6 -1 -4 -2 3 -2 -7 6 1 2-6 -4 -2 3 -2-7 6 1 2 6 Ax3 = 0 3 100 JT 000 I 1 IT L 43- 12*2 0 3 -11 -3 1 2 d1x1 A3*3

AX1 AX2 -4-2 3 1 СЕВЕ -2-7 6 2 1 2 6 -1 -4 -2 3 -2 -7 6 1 2-6 -4 -2 3 -2-7 6 1 2 6 Ax3 = 0 3 100 JT 000 I 1 IT L 43- 12*2 0 3 -11 -3 1 2 d1x1 A3*3

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 ; is an eigenvalue of A and that x; is a corresponding eigenvector. -4 -2 3 A = -2 -7 6 A₁ = -11, x₁ = (1, 2, -1) 2₂= = -3, x2 = (-2, 10) = -3, x3 = (3, 0, 1) 1 2 -6 13 = -11 = 2₁x₁ 12x2 Ax1 = Ax2 = Ax3 = -4 -2 3 -2 -7 6 1 2 6 -4 -2 3 -2 -7 w 1 2 -1 I -2 = 1 = 0 6 1 2 -6 -4 -2 3 3 -2 -7 6 0 = 1 2 -6 1 00 ↓↑ 000 ↓↑ 000 11 ↓ T 1 2 -1 -2 [1] 0 3 -8 - -3 = 1 = 13x3
Transcribed Image Text:Verify that ; is an eigenvalue of A and that x; is a corresponding eigenvector. -4 -2 3 A = -2 -7 6 A₁ = -11, x₁ = (1, 2, -1) 2₂= = -3, x2 = (-2, 10) = -3, x3 = (3, 0, 1) 1 2 -6 13 = -11 = 2₁x₁ 12x2 Ax1 = Ax2 = Ax3 = -4 -2 3 -2 -7 6 1 2 6 -4 -2 3 -2 -7 w 1 2 -1 I -2 = 1 = 0 6 1 2 -6 -4 -2 3 3 -2 -7 6 0 = 1 2 -6 1 00 ↓↑ 000 ↓↑ 000 11 ↓ T 1 2 -1 -2 [1] 0 3 -8 - -3 = 1 = 13x3
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