A is a 5 x 5 matrix with two eigenvalues. One eigenspace is three-dimensional, and the other eigenspace is two- dimensional. Is A diagonalizable? Why?
A is a 5 x 5 matrix with two eigenvalues. One eigenspace is three-dimensional, and the other eigenspace is two- dimensional. Is A diagonalizable? Why?
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
23 pl
![In
try
you
these exercises.)
Mark each statement True or False. Justify each answer. (Study
Exercises 21 and 22, A, B, P, and D are nxn matrices.
Theorems 5 and 6 and the examples in this section carefully before
(
21. a. A is diagonalizable if A = PDP-1 for some matrix D
and some invertible matrix P.
nalizable.
b. If R" has a basis of eigenvectors of A, then A is diago-
2
MD
counting multiplicities.
A is diagonalizable if and only if A has n eigenvalues,
d. If A is diagonalizable, then A is invertible.
in
ASO
D₁P
30. With A and
to the P in
igns Mu
31. Construct a
diagonaliz
32. Construct
but not in
c. If AP = PD, with D diagonal, then the nonzero columns
of P must be eigenvectors of A.
d. If A is invertible, then A is diagonalizable.
22. a. A is diagonalizable if A has n eigenvectors.
b. If A is diagonalizable, then A has n distinct eigenvalues. 35.
THAUS
[M] Diagonal
trix program
then compute
23. A is a 5 x 5 matrix with two eigenvalues. One eigenspace
is three-dimensional, and the other eigenspace is two-
dimensional. Is A diagonalizable? Why?
33.
-6
-3
-1
36.
11
-3
-8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22b1319c-242c-4915-8f56-7c035e43f773%2F2584a675-2d92-43bc-bbc7-ad9c654f2409%2Fn8bampt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In
try
you
these exercises.)
Mark each statement True or False. Justify each answer. (Study
Exercises 21 and 22, A, B, P, and D are nxn matrices.
Theorems 5 and 6 and the examples in this section carefully before
(
21. a. A is diagonalizable if A = PDP-1 for some matrix D
and some invertible matrix P.
nalizable.
b. If R" has a basis of eigenvectors of A, then A is diago-
2
MD
counting multiplicities.
A is diagonalizable if and only if A has n eigenvalues,
d. If A is diagonalizable, then A is invertible.
in
ASO
D₁P
30. With A and
to the P in
igns Mu
31. Construct a
diagonaliz
32. Construct
but not in
c. If AP = PD, with D diagonal, then the nonzero columns
of P must be eigenvectors of A.
d. If A is invertible, then A is diagonalizable.
22. a. A is diagonalizable if A has n eigenvectors.
b. If A is diagonalizable, then A has n distinct eigenvalues. 35.
THAUS
[M] Diagonal
trix program
then compute
23. A is a 5 x 5 matrix with two eigenvalues. One eigenspace
is three-dimensional, and the other eigenspace is two-
dimensional. Is A diagonalizable? Why?
33.
-6
-3
-1
36.
11
-3
-8
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