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
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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Assignment 9 Section 5.1:4(b) only!!
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ea26e8a-300c-48ec-9a67-e6dff583b7a5%2Fa71eb314-2d72-4d12-a927-5d42c013080f%2Fwy3b0q_processed.png&w=3840&q=75)
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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