ection 5.1 Number 4(b) only with perfectly and com
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
Section 5.1 Number 4(b) only with perfectly and complete explanations.
Transcribed Image Text:258
4. For each of the following matrices A Є Mnxn (F),
(i) Determine all the eigenvalues of A.
(ii) For each eigenvalue A of A, find the set of eigenvectors correspond-
ing to A.
(iii) If possible, find a basis for F" consisting of eigenvectors of A.
(iv) If successful in finding such a basis, determine an invertible matrix
Q and a diagonal matrix D such that Q¹AQ = D.
Chap. 5 Diagonalization
1 2
(a) A=
for F
= R
3
2
0
-2
(b) A =
=
1
-1
for F = R
2
2
5
(c) A=
(2 ½)
for F = C
2 0
-1
(d) A
4
1 -4
for FR
0 -1
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