Given matrix F as follows. [9 F = 4 L8 4 8 15 -4 -4 9 a) Use the Gerschgorin's Circle Theorem to determine region of all the eigenvalues of F. State the biggest circle. b) Find the dominant eigenvalue (2₁) and the corresponding eigenvector of matrix F using Power method. Use v(0) = [1, 1, 1]. Do calculations in 3 decimal points and ε = 0.001. c) If the smallest eigenvalue A3 = 5, find the intermediate eigenvalue of matrix F.

Given matrix F as follows. [9 F = 4 L8 4 8 15 -4 -4 9 a) Use the Gerschgorin's Circle Theorem to determine region of all the eigenvalues of F. State the biggest circle. b) Find the dominant eigenvalue (2₁) and the corresponding eigenvector of matrix F using Power method. Use v(0) = [1, 1, 1]. Do calculations in 3 decimal points and ε = 0.001. c) If the smallest eigenvalue A3 = 5, find the intermediate eigenvalue of matrix F.

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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