Question 2 Give a matrix A as follows -2-6 0 A = 2 7 0 1 2 -1 a) Find the polynomial characteristics of matrix A b) Use the Gerschgorin's circle theorem to determine a region containing all the eigenvalues of A. Find the dominant eigenvalue (2) and the corresponding eigenvector of matrix A using the power method. Use (0) = [0, 1, 1]. Do calculation accurate to & = 0.05 d) Suppose the smallest eigenvalue (23) of matrix A is -3. Find the intermediate eigenvalue.
Question 2 Give a matrix A as follows -2-6 0 A = 2 7 0 1 2 -1 a) Find the polynomial characteristics of matrix A b) Use the Gerschgorin's circle theorem to determine a region containing all the eigenvalues of A. Find the dominant eigenvalue (2) and the corresponding eigenvector of matrix A using the power method. Use (0) = [0, 1, 1]. Do calculation accurate to & = 0.05 d) Suppose the smallest eigenvalue (23) of matrix A is -3. Find the intermediate eigenvalue.
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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![Question 2
Give a matrix A as follows
-2
-60
A =
2
7
0
1
2
a) Find the polynomial characteristics of matrix A
b)
Use the Gerschgorin's circle theorem to determine a region containing all the eigenvalues of
A.
c)
Find the dominant eigenvalue (,) and the corresponding eigenvector of matrix A using the
power method. Use v) = [0, 1, 1]. Do calculation accurate to ε = 0.05
&
d)
Suppose the smallest eigenvalue (23) of matrix A is -3. Find the intermediate eigenvalue.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F079634c6-3ae6-4122-875d-c634b9247d26%2F965cab45-5e8c-4c75-868f-db0461b4a464%2Faz5v0dr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 2
Give a matrix A as follows
-2
-60
A =
2
7
0
1
2
a) Find the polynomial characteristics of matrix A
b)
Use the Gerschgorin's circle theorem to determine a region containing all the eigenvalues of
A.
c)
Find the dominant eigenvalue (,) and the corresponding eigenvector of matrix A using the
power method. Use v) = [0, 1, 1]. Do calculation accurate to ε = 0.05
&
d)
Suppose the smallest eigenvalue (23) of matrix A is -3. Find the intermediate eigenvalue.
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