1.5.3The symmetric matrix31 1A = 1 3 11 1 5has dominant eigenvector e₁ = [1 1 2]¹.Obtain the matrixA₁ = A - λ₁êêwhere 2, is the eigenvalue corresponding to theeigenvector e₁. Using the deflation method, obtainthe subdominant eigenvalue λ, and correspondingeigenvector e, correct to two decimal places, taking[111] as a first approximation to e₂. Continuethe process to obtain the third eigenvalue 23 and itscorresponding eigenvector €3.

Here, we are given with symmetric matrix. We need to use deflection method to solve this problem.

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

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 8BEXP

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