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The symmetric matrix 3 11 A = 1 3 1 115 has dominant eigenvector e, = [1 1 2]¹. Obtain the matrix A₁ = A - λ₁e₁e¹ where 2, is the eigenvalue corresponding to the eigenvector e₁. Using the deflation method, obtain the subdominant eigenvalue 2₂ and corresponding eigenvector e, correct to two decimal places, taking [111] as a first approximation to e₂. Continue the process to obtain the third eigenvalue 23 and its corresponding eigenvector e3.

The symmetric matrix 3 11 A = 1 3 1 115 has dominant eigenvector e, = [1 1 2]¹. Obtain the matrix A₁ = A - λ₁e₁e¹ where 2, is the eigenvalue corresponding to the eigenvector e₁. Using the deflation method, obtain the subdominant eigenvalue 2₂ and corresponding eigenvector e, correct to two decimal places, taking [111] as a first approximation to e₂. Continue the process to obtain the third eigenvalue 23 and its corresponding eigenvector e3.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 24EQ
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1.5.3 The symmetric matrix 31 1 A = 1 3 1 1 1 5 has dominant eigenvector e₁ = [1 1 2]¹. Obtain the matrix A₁ = A - λ₁êê where 2, is the eigenvalue corresponding to the eigenvector e₁. Using the deflation method, obtain the subdominant eigenvalue λ, and corresponding eigenvector e, correct to two decimal places, taking [111] as a first approximation to e₂. Continue the process to obtain the third eigenvalue 23 and its corresponding eigenvector €3.
Transcribed Image Text:1.5.3 The symmetric matrix 31 1 A = 1 3 1 1 1 5 has dominant eigenvector e₁ = [1 1 2]¹. Obtain the matrix A₁ = A - λ₁êê where 2, is the eigenvalue corresponding to the eigenvector e₁. Using the deflation method, obtain the subdominant eigenvalue λ, and corresponding eigenvector e, correct to two decimal places, taking [111] as a first approximation to e₂. Continue the process to obtain the third eigenvalue 23 and its corresponding eigenvector €3.
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