(2) Same problem with A 1 0 0 1 0 0 0 0 -2 0 1 -2 0 −1 -2 -2 - -
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
jj1.
Problem No.2 plz!
![(1) Compute the rational canonical form for
-1 −1 -1
-2 0 −1
6 3 4
A =
That is, present it as SRS-¹, where R consists of companion ma-
trix blocks along the diagonal and S is a change-of-basis matrix.
Interpret the result in terms of a direct-sum decomposition of R³
under the action of the transformation T with matrix [T]ê = A.
(2) Same problem with
A =
1
0
A =
0
0 0
1 0 0
0 1
0 -1 -2
-2 -2
-2
and R4 instead of R³. [Note: from Exercise VI.B.2(a), you already
know the normal form for AI4 – A.]
(3) Once more, same problem with
How does it depend on c?
1000
c100
0c10
00c1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d0e6bf9-348c-40ab-ae4c-488cbc0bf710%2F40816862-23ea-4f54-9ef1-cb0fdd0107d9%2F6jfz7y_processed.png&w=3840&q=75)
Transcribed Image Text:(1) Compute the rational canonical form for
-1 −1 -1
-2 0 −1
6 3 4
A =
That is, present it as SRS-¹, where R consists of companion ma-
trix blocks along the diagonal and S is a change-of-basis matrix.
Interpret the result in terms of a direct-sum decomposition of R³
under the action of the transformation T with matrix [T]ê = A.
(2) Same problem with
A =
1
0
A =
0
0 0
1 0 0
0 1
0 -1 -2
-2 -2
-2
and R4 instead of R³. [Note: from Exercise VI.B.2(a), you already
know the normal form for AI4 – A.]
(3) Once more, same problem with
How does it depend on c?
1000
c100
0c10
00c1
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