1. Given the matrix 5 -2 1 A =-2 30 1 06 has three eigenvalues, A,, A2, and Ag in such that A> |2 > Aal. i. If A = 7, compute the smallest eigenvalue, Ag and its corresponding eigenvector, v3 by using shifted power method. Use v(0) = (0.5, 1, 0)T and stop the iteration when Im+1- ma <0.05. Do all calculation in two decimal places. ii. Using results in part (i), determine the other eigenvalue, A2 of A.
1. Given the matrix 5 -2 1 A =-2 30 1 06 has three eigenvalues, A,, A2, and Ag in such that A> |2 > Aal. i. If A = 7, compute the smallest eigenvalue, Ag and its corresponding eigenvector, v3 by using shifted power method. Use v(0) = (0.5, 1, 0)T and stop the iteration when Im+1- ma <0.05. Do all calculation in two decimal places. ii. Using results in part (i), determine the other eigenvalue, A2 of A.
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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Transcribed Image Text:1.
Given the matrix
-2 1
A
-2 3 0
1
0 6
has three eigenvalues, A1, A2, and Ag in such that A>A2l > |Agl.
i. If A = 7, compute the smallest eigenvalue, Ag and its corresponding
eigenvector, v3 by using shifted power method. Use v(0) = (0.5, 1, 0)T
and stop the iteration when Im+1- mal < 0.05. Do all calculation
in two decimal places.
ii. Using results in part (i), determine the other eigenvalue, A2 of A.
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