(a) Using the power method find the dominant eigenvalue and the corresponding eigenvector of the matrix 2 1 A 1 2.5 1 11 3 starting with an initial vector [111] and working to three decimal places. (b) Given that another eigenvalue of A is 1.19 correct to two decimal places, find the value of the third eigenvalue using a property of matrices. (c) Having determined all the eigenvalues of A, indicate which of these can be obtained by using the power method on the following matrices: (i) A-¹; (ii) A - 31.
(a) Using the power method find the dominant eigenvalue and the corresponding eigenvector of the matrix 2 1 A 1 2.5 1 11 3 starting with an initial vector [111] and working to three decimal places. (b) Given that another eigenvalue of A is 1.19 correct to two decimal places, find the value of the third eigenvalue using a property of matrices. (c) Having determined all the eigenvalues of A, indicate which of these can be obtained by using the power method on the following matrices: (i) A-¹; (ii) A - 31.
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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Solve all
![(a) Using the power method find the dominant
eigenvalue and the corresponding eigenvector
of the matrix
21
A = 12.5 1
1 1 3
starting with an initial vector [111]
and working to three decimal places.
(b) Given that another eigenvalue of A is 1.19
correct to two decimal places, find the value of the
third eigenvalue using a property of matrices.
(c) Having determined all the eigenvalues of A,
indicate which of these can be obtained by
using the power method on the following
matrices: (i) A-¹; (ii) A - 31.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8222824-b0b2-4366-bd51-0b90537c8121%2F4e4718c9-0158-440e-ae99-86f6540a7e9b%2F872mvjt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Using the power method find the dominant
eigenvalue and the corresponding eigenvector
of the matrix
21
A = 12.5 1
1 1 3
starting with an initial vector [111]
and working to three decimal places.
(b) Given that another eigenvalue of A is 1.19
correct to two decimal places, find the value of the
third eigenvalue using a property of matrices.
(c) Having determined all the eigenvalues of A,
indicate which of these can be obtained by
using the power method on the following
matrices: (i) A-¹; (ii) A - 31.
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