Let the characteristic polynomial of A be X=(8-5) (8-2)² and the minimal polynomial be (8-5)² (8-2) Find all possible Jordan forms J for the matrix A 201 000 0 a 51

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.3: Properties Of Determinants
Problem 63E: Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.
icon
Related questions
Question
Let the characteristic polynomial of A be
x = (8-5) (8 - 2)2
and the minimal polynomial be
(8-5)² (8-2)
Find all possible Jordan forms J for the matrix A
О
either J
either J
either J
510000
ОБ000 0
005100
000500
0 000 20
00000 2
[510000
050000
005000
000 5 0 0
000020
00000 2,
[510000
0500
0051 0 0
000500
0
0 20
0 0
0 0 0
00
0 0 0 0 0 2
ГБ 1
0600 0
0000
0
005 10 0
or J
oe J
5 1000
000090
0 0 6 0 0 0
0005 00
000020
000002
5000 001
050000
005000
000 50 0
000020
0000 03
[510000
05 0 0 0 0
005000
009000
1G00 00
0
2
000002
510000
050000
05000
Transcribed Image Text:Let the characteristic polynomial of A be x = (8-5) (8 - 2)2 and the minimal polynomial be (8-5)² (8-2) Find all possible Jordan forms J for the matrix A О either J either J either J 510000 ОБ000 0 005100 000500 0 000 20 00000 2 [510000 050000 005000 000 5 0 0 000020 00000 2, [510000 0500 0051 0 0 000500 0 0 20 0 0 0 0 0 00 0 0 0 0 0 2 ГБ 1 0600 0 0000 0 005 10 0 or J oe J 5 1000 000090 0 0 6 0 0 0 0005 00 000020 000002 5000 001 050000 005000 000 50 0 000020 0000 03 [510000 05 0 0 0 0 005000 009000 1G00 00 0 2 000002 510000 050000 05000
either J
either J
either Ja
or J
000020
0 0 0 0 0 2
510000
05 0 0 0 0
0 0 50 00
000500
000020
0 0 000 2
510000
05 0 0 0 0
0
005100
000500
000020
0 0 0 0 0 2
5 1000 07
050000
005 100
000500
000020
0
51
05
0
0
0 0
0 0 0 0 2
0 0 5100
0500
0021
0 0 0 0
0 0 0 0
0 0 0 0 0 2
20000
or J-
or J
or J=
or J-
00002
000 00
500000
050000
000 90 0
SN
0 0 5 0 0 0
000500
000020
00000 2
0 2,
510000
050000
005000
000500
000021
0 0 0 0 0
050000
005000
51000
050000
005000
000500
000020
L00000 2,
100007
0 0 0
0 0 0
0
009
021
0 0 0 0 2
Transcribed Image Text:either J either J either Ja or J 000020 0 0 0 0 0 2 510000 05 0 0 0 0 0 0 50 00 000500 000020 0 0 000 2 510000 05 0 0 0 0 0 005100 000500 000020 0 0 0 0 0 2 5 1000 07 050000 005 100 000500 000020 0 51 05 0 0 0 0 0 0 0 0 2 0 0 5100 0500 0021 0 0 0 0 0 0 0 0 0 0 0 0 0 2 20000 or J- or J or J= or J- 00002 000 00 500000 050000 000 90 0 SN 0 0 5 0 0 0 000500 000020 00000 2 0 2, 510000 050000 005000 000500 000021 0 0 0 0 0 050000 005000 51000 050000 005000 000500 000020 L00000 2, 100007 0 0 0 0 0 0 0 009 021 0 0 0 0 2
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage