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Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. -4-2 2₁-11, x₁ = (1, 2, -1) = A = -2 -7 A₂ = -3, x₂ = (-2, 10) A3 = -3, x3 = (3, 0, 1) 1 2-6 -4-2 3 AX1 -FPBD- -2-7 6 2 = = -11 2 21x1 1 2-6 -4-2 3 -3 -#-+- AX2 -2 -7 = = 2₂x₂ 6 1 2-6 3 -4 -2 -2 -7 6 El Ax3 = = 36 1 = = 13x3

Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. -4-2 2₁-11, x₁ = (1, 2, -1) = A = -2 -7 A₂ = -3, x₂ = (-2, 10) A3 = -3, x3 = (3, 0, 1) 1 2-6 -4-2 3 AX1 -FPBD- -2-7 6 2 = = -11 2 21x1 1 2-6 -4-2 3 -3 -#-+- AX2 -2 -7 = = 2₂x₂ 6 1 2-6 3 -4 -2 -2 -7 6 El Ax3 = = 36 1 = = 13x3

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 4EQ: In Exercises 1-6, show that vis an eigenvector of A and find the corresponding eigenvalue....
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Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. -4 -2 3 2₁-11, x₁ = (1, 2, -1) = A = -2 -7 6 2₂ = -3, x₂ = (-2, 10) 23 = -3, x3 = (3, 0, 1) 1 2 -6 -4-2 3 AX1 = -2 -7 6 2 = = 21x1 1 2 -6 -1 -2 AX2 -4 -2 3 -2 -7 6 2 -6 1 = 1 -4-2 3 3 -RDE Ax3 = -2 -7 6 0 = 1 2-6 1 I ↓ ↑ 11 = 11 -=[ -1 -2 0 3 -3 -[1] - = = λ3x3 -3 H = 22x2
Transcribed Image Text:Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. -4 -2 3 2₁-11, x₁ = (1, 2, -1) = A = -2 -7 6 2₂ = -3, x₂ = (-2, 10) 23 = -3, x3 = (3, 0, 1) 1 2 -6 -4-2 3 AX1 = -2 -7 6 2 = = 21x1 1 2 -6 -1 -2 AX2 -4 -2 3 -2 -7 6 2 -6 1 = 1 -4-2 3 3 -RDE Ax3 = -2 -7 6 0 = 1 2-6 1 I ↓ ↑ 11 = 11 -=[ -1 -2 0 3 -3 -[1] - = = λ3x3 -3 H = 22x2
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