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Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. A₁ = -11, x₁ = (1, 2,−1) −3, x₂ = (-2, 10) λ₂ = λ3 = −3, x3 = (3, 0, 1) Ax1 Ax2 = A = Ax3 -4 -2 3 -2 -7 6 1 2-6 -4 -2 3 -2 -7 6 1 2-6 -2 -7 1 2 1 2 -1 -4 -2 -2 -7 6 1 2-6 -4 -2 3 -2 -609-40- 1 = I 3 3 [:] 1 = 0 = 1 []- 2 = = -11 = -3 21x1 -2 1 = 12x2 3 -H -3 0 = 13x3

Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. A₁ = -11, x₁ = (1, 2,−1) −3, x₂ = (-2, 10) λ₂ = λ3 = −3, x3 = (3, 0, 1) Ax1 Ax2 = A = Ax3 -4 -2 3 -2 -7 6 1 2-6 -4 -2 3 -2 -7 6 1 2-6 -2 -7 1 2 1 2 -1 -4 -2 -2 -7 6 1 2-6 -4 -2 3 -2 -609-40- 1 = I 3 3 [:] 1 = 0 = 1 []- 2 = = -11 = -3 21x1 -2 1 = 12x2 3 -H -3 0 = 13x3

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 λ; is an eigenvalue of A and that x; is a corresponding eigenvector. A₁ = -11, X₁ = (1, 2, −1) λ₂ = −3, x₂ = (–2, 10) 13 = -3, x3 = (3, 0, 1) A = -4 -2 3 -2 -7 6, Ax3 1 2 -6 -4 -2 -630- Ax₁ = -2 -7 1 2-6 -1 1 2 = -4 -2 3 -2 -EU- Ax₂ = -2 -7 6 1 1 2-6 0 = -4 -2 3 3 -RDE -2 -7 = 6 1 2-6 1 ↓ 1 ↓ 1 = -11 = -3 -3 1 2 -1 -2 1 0 O = λιX1 = 1₂x2 = 13x3
Transcribed Image Text:Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. A₁ = -11, X₁ = (1, 2, −1) λ₂ = −3, x₂ = (–2, 10) 13 = -3, x3 = (3, 0, 1) A = -4 -2 3 -2 -7 6, Ax3 1 2 -6 -4 -2 -630- Ax₁ = -2 -7 1 2-6 -1 1 2 = -4 -2 3 -2 -EU- Ax₂ = -2 -7 6 1 1 2-6 0 = -4 -2 3 3 -RDE -2 -7 = 6 1 2-6 1 ↓ 1 ↓ 1 = -11 = -3 -3 1 2 -1 -2 1 0 O = λιX1 = 1₂x2 = 13x3
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