eigenvalues and their corresponding eigen vectors

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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In-Class Exercise 6
A set of linear equations is given:
10 x₁ + 4x₂ - 2x3 = 26
4x₁ - 8x₂ + x3 = 0
2
2x₁ + x₂ - 5x3 = 40
4
1) Solve the equations by using Gauss-Seidel iterative method. Do it
"by hand" (you can use matlab for arithmetic calculations). Start
with guessing answer [X1 X2 X3] = [0 0 0] and try at least three
iterations.
2) Use power method to find the smallest eigenvalue of the
coefficient matrix. (hint: use inverse of coefficient matrix, then
apply power method to find largest eigenvalue. Take inverse of
that eigenvalue)
3) Find all eigenvalues and their corresponding eigen vectors of the
coefficient matrix.
Transcribed Image Text:In-Class Exercise 6 A set of linear equations is given: 10 x₁ + 4x₂ - 2x3 = 26 4x₁ - 8x₂ + x3 = 0 2 2x₁ + x₂ - 5x3 = 40 4 1) Solve the equations by using Gauss-Seidel iterative method. Do it "by hand" (you can use matlab for arithmetic calculations). Start with guessing answer [X1 X2 X3] = [0 0 0] and try at least three iterations. 2) Use power method to find the smallest eigenvalue of the coefficient matrix. (hint: use inverse of coefficient matrix, then apply power method to find largest eigenvalue. Take inverse of that eigenvalue) 3) Find all eigenvalues and their corresponding eigen vectors of the coefficient matrix.
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