Suppose B is a 7-by-7 matrix with characteristic polynomial(A – 1) (A – 4)²|Also, assume the following is known about $B$:The nullity of B-l is 3.The nullity of B-4l is 1The nullity of (B-1)2 is 4.Which of the following is the Jordan canonical form of B? 1 0 0 0 00 1 1 0 0 0 o0 0 1 0 0 0 00 0 0 1 0 0 00 0 0 0 1 0 00 0 0 0 0 4 1_0 0 0 0 0 0 4_1o [1 1 0 0 0 0 00 1 10 0 0 00 0 1 0 0 0 00 0 0 1 0 0 00 0 0 0 1 0 00 0 0 0 0 40Lo o 0 0 0 0 .[1 1 0 0 0 0 010 1 0 0 0 0 00 0 1 1 0 0 00 0 0 1 0 0 00 0 0 0 1 0 00 0 0 0 0 4 0_0 0 0 0 0 0 4.o [1 1 0 0 0 0 00 1 0 0 0 0 o0 0 1 1 0 0 00 0 0 10 0 00 0 0 0 1 0 00 0 0 0 0 4 1Lo o 0 00 0 4]o [1 0 0 0 o o 0°0 0 00 1 0 00 0 10 0 0 00 0 0 1 0 0 00 0 0 0 1 0 00 4 00 0 0 00 0 0 0 0 0 4]

Result: The total number of Jordan blocks corresponding to λi's equal to geometric multiplicities of…

Suppose B is a 7-by-7 matrix with characteristic polynomial (A – 1)* (A – 4)² Also, assume the following is known about $B$: The nullity of B-l is 3. The nullity of B-4l is 1 The nullity of (B-1)2 is 4. Which of the following is the Jordan canonical form of B?

Suppose B is a 7-by-7 matrix with characteristic polynomial (A – 1)* (A – 4)² Also, assume the following is known about $B$: The nullity of B-l is 3. The nullity of B-4l is 1 The nullity of (B-1)2 is 4. Which of the following is the Jordan canonical form of B?

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

Suppose B is a 7-by-7 matrix with characteristic polynomial
(A – 1) (A – 4)²
|
Also, assume the following is known about $B$:
The nullity of B-l is 3.
The nullity of B-4l is 1
The nullity of (B-1)2 is 4.
Which of the following is the Jordan canonical form of B?

1 0 0 0 0
0 1 1 0 0 0 o
0 0 1 0 0 0 0
0 0 0 1 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 4 1
_0 0 0 0 0 0 4_
1
o [1 1 0 0 0 0 0
0 1 1
0 0 0 0
0 0 1 0 0 0 0
0 0 0 1 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 40
Lo o 0 0 0 0 .
[1 1 0 0 0 0 01
0 1 0 0 0 0 0
0 0 1 1 0 0 0
0 0 0 1 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 4 0
_0 0 0 0 0 0 4.
o [1 1 0 0 0 0 0
0 1 0 0 0 0 o
0 0 1 1 0 0 0
0 0 0 10 0 0
0 0 0 0 1 0 0
0 0 0 0 0 4 1
Lo o 0 0
0 0 4]
o [1 0 0 0 o o 0°
0 0 0
0 1 0 0
0 0 10 0 0 0
0 0 0 1 0 0 0
0 0 0 0 1 0 0
0 4 0
0 0 0 0
0 0 0 0 0 0 4]

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