the matrix 20 A-2 1 2 1 3 1 nd the bounds for the eigenvalues of matrix A. Draw the associated Gersgorin rcle diagram. et A₁7 and ₁ = (1 1 1 ) be dominant eigenvalue and eigenvector of A, spectively. Compute 3 iterations of the power method to approximate a second genvector 2 and eigenvalue >₂.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.5: Iterative Methods For Computing Eigenvalues
Problem 6EQ
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Given the matrix
A =
-2 12
1 3 1
5.1 Find the bounds for the eigenvalues of matrix A. Draw the associated Gersgorin
circle diagram.
5.2 Let A₁ = 7 and ₁ = (1 1 1) be dominant eigenvalue and eigenvector of A,
respectively. Compute 3 iterations of the power method to approximate a second
eigenvector 2 and eigenvalue >₂.
Transcribed Image Text:Given the matrix A = -2 12 1 3 1 5.1 Find the bounds for the eigenvalues of matrix A. Draw the associated Gersgorin circle diagram. 5.2 Let A₁ = 7 and ₁ = (1 1 1) be dominant eigenvalue and eigenvector of A, respectively. Compute 3 iterations of the power method to approximate a second eigenvector 2 and eigenvalue >₂.
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