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Question 39 - Week 1 Practice | Prasnya
Q39
00:00
16 Jul 2023
Q39.
Which of the following matrices satisfy
A
k
=
0
A^k=0
A
k
=
0
for some natural number
k
k
k
?
A
[
4
−
4
0
0
4
−
4
0
0
0
0
4
−
4
0
0
4
−
4
]
\begin{bmatrix}4&-4&0&0\\4&-4&0&0\\0&0&4&-4\\0&0&4&-4\end{bmatrix}
4
4
0
0
−
4
−
4
0
0
0
0
4
4
0
0
−
4
−
4
B
[
0
3
2
1
0
0
2
2
0
0
0
3
0
0
0
0
]
\begin{bmatrix}0&3&2&1\\0&0&2&2\\0&0&0&3\\0&0&0&0\end{bmatrix}
0
0
0
0
3
0
0
0
2
2
0
0
1
2
3
0
C
[
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
]
\begin{bmatrix}0&1&1&1\\1&0&1&1\\1&1&0&1\\1&1&1&0\end{bmatrix}
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
D
[
−
1
0
0
1
0
−
1
0
2
0
0
−
1
2
1
0
0
0
]
\begin{bmatrix}-1&0&0&1\\0&-1&0&2\\0&0&-1&2\\1&0&0&0\end{bmatrix}
−
1
0
0
1
0
−
1
0
0
0
0
−
1
0
1
2
2
0
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Q39
00:00
16 Jul 2023
Q39.
Which of the following matrices satisfy
A
k
=
0
A^k=0
A
k
=
0
for some natural number
k
k
k
?
A
[
4
−
4
0
0
4
−
4
0
0
0
0
4
−
4
0
0
4
−
4
]
\begin{bmatrix}4&-4&0&0\\4&-4&0&0\\0&0&4&-4\\0&0&4&-4\end{bmatrix}
4
4
0
0
−
4
−
4
0
0
0
0
4
4
0
0
−
4
−
4
B
[
0
3
2
1
0
0
2
2
0
0
0
3
0
0
0
0
]
\begin{bmatrix}0&3&2&1\\0&0&2&2\\0&0&0&3\\0&0&0&0\end{bmatrix}
0
0
0
0
3
0
0
0
2
2
0
0
1
2
3
0
C
[
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
]
\begin{bmatrix}0&1&1&1\\1&0&1&1\\1&1&0&1\\1&1&1&0\end{bmatrix}
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
D
[
−
1
0
0
1
0
−
1
0
2
0
0
−
1
2
1
0
0
0
]
\begin{bmatrix}-1&0&0&1\\0&-1&0&2\\0&0&-1&2\\1&0&0&0\end{bmatrix}
−
1
0
0
1
0
−
1
0
0
0
0
−
1
0
1
2
2
0
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