4 2 4 0 2 -1 0 Suppose that A = Find the eigenvalues of A, i.e. 3 %3D 0 0 3 0 4 the A which satisfies det|A – AI4| = 0. 7 The eigenvalues of A is listed as follows in order from biggest to smallest: || I|||

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section: Chapter Questions
Problem 7RQ
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4 2
0 4
0 2
1 0
-
Suppose that A =
Find the eigenvalues of A, i.e.
3
0 0
3
0 4
the A which satisfies det A – AI4| = 0.
7
-
The eigenvalues of A is listed as follows in order from biggest to
smallest:
||
Transcribed Image Text:4 2 0 4 0 2 1 0 - Suppose that A = Find the eigenvalues of A, i.e. 3 0 0 3 0 4 the A which satisfies det A – AI4| = 0. 7 - The eigenvalues of A is listed as follows in order from biggest to smallest: ||
2 0 0
Suppose that A =
-2 1
ㅇ
Find the eigenvectors of A
1
-1
(a) Eigenvector with respect to the smallest eigenvalue: v1
where v1 is a unit vector;
(b) Eigenvector with respect to the second smallest eigenvalue:
V2
where v2 is a unit vector;
(c) Eigenvector with respect to the bigest eigenvalue: v3
where vz is a unit vector.
Transcribed Image Text:2 0 0 Suppose that A = -2 1 ㅇ Find the eigenvectors of A 1 -1 (a) Eigenvector with respect to the smallest eigenvalue: v1 where v1 is a unit vector; (b) Eigenvector with respect to the second smallest eigenvalue: V2 where v2 is a unit vector; (c) Eigenvector with respect to the bigest eigenvalue: v3 where vz is a unit vector.
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