Given matrix F as follows. [4 F = 9 L8 15 -17 4 8 -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, 0]. Do calculations in 3 decimal points and ε = 0.01. c) If the smallest eigenvalue A3 = -5, find the intermediate eigenvalue of matrix F.
Given matrix F as follows. [4 F = 9 L8 15 -17 4 8 -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, 0]. Do calculations in 3 decimal points and ε = 0.01. c) If the smallest eigenvalue A3 = -5, find the intermediate eigenvalue of matrix F.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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q1
![Given matrix F as follows.
[4
F = 9
L8
15 -1
4 8
-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, 0]. Do calculations in 3 decimal points and
ε = 0.01.
c) If the smallest eigenvalue 13 = −5, find the intermediate eigenvalue of matrix F.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F369eb33d-5550-4191-a702-94922b8cf6c1%2F30b53029-0a0a-43b3-bdb0-544eca4e42ea%2F0ku82jf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given matrix F as follows.
[4
F = 9
L8
15 -1
4 8
-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, 0]. Do calculations in 3 decimal points and
ε = 0.01.
c) If the smallest eigenvalue 13 = −5, find the intermediate eigenvalue of matrix F.
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