Using NumPy, write the program that determines whether the A=({{1, 5, -2}, {1, 2, -1}, {3, 6, -3}}) matrix is nilpotent.
Using NumPy, write the program that determines whether the A=({{1, 5, -2}, {1, 2, -1}, {3, 6, -3}}) matrix is nilpotent.
Computer Networking: A Top-Down Approach (7th Edition)
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Using NumPy, write the program that determines whether the A=({{1, 5, -2}, {1, 2, -1}, {3, 6, -3}}) matrix is nilpotent.
Itro: Nilpotent Matrix: A square matrix A is called nilpotent matrix of order k provided it satisfies the relation, Ak = O and Ak-1≠O where k is a positive integer & O is a null matrix of order k and k is the order of the nilpotent matrix A .
The following picture is an example of the intro:
Ps: Please also explain step by step with " # "
![Hence, the matrix A is nilpotent of order 3.
1
3
| Example 17. show that
6 is nilpotent
-2 -1
-3
matrix of order 3.
1
1
Sol. Let A =
2
-2
-1
-3
1 1
1
3
A = A A =|
5 2
6 X 5
6.
-2
-1
-3
-1
-3
1+5-6
1+ 2-3
3+6-9
5+ 10 – 12
5 + 4 - 6
15 + 12 - 18
|- 2-5+ 6
- 2 – 2 + 3 - 6 – 6 + 9 |
3
-1
-1
-3
HE
0.
1 1
:. A = A? . A =
3
3
9.
-1
-1
-3
-2
-1
-3
0 +0+0
To o o
0 +0+0
0+0+0
= 3 + 15 - 18
00 0=0
(-3)]
3+6-9
%3D
9 + 18- 27
000
-3)
-1-5+6 -1-2+3 - 3- 6 +9]
(-3)]
A = O ie., A = o
Here,
k = 3
2)
1,
2.
2.
3.
3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2fe44a2-ce5a-4705-99b2-8367a19f4f0d%2Fca738e4c-e997-4caf-82e6-cae79009e1b8%2Fo3d6ozj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Hence, the matrix A is nilpotent of order 3.
1
3
| Example 17. show that
6 is nilpotent
-2 -1
-3
matrix of order 3.
1
1
Sol. Let A =
2
-2
-1
-3
1 1
1
3
A = A A =|
5 2
6 X 5
6.
-2
-1
-3
-1
-3
1+5-6
1+ 2-3
3+6-9
5+ 10 – 12
5 + 4 - 6
15 + 12 - 18
|- 2-5+ 6
- 2 – 2 + 3 - 6 – 6 + 9 |
3
-1
-1
-3
HE
0.
1 1
:. A = A? . A =
3
3
9.
-1
-1
-3
-2
-1
-3
0 +0+0
To o o
0 +0+0
0+0+0
= 3 + 15 - 18
00 0=0
(-3)]
3+6-9
%3D
9 + 18- 27
000
-3)
-1-5+6 -1-2+3 - 3- 6 +9]
(-3)]
A = O ie., A = o
Here,
k = 3
2)
1,
2.
2.
3.
3.
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