Question 39 - Week 4 Practice | Prasnya
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Week 4
Question 39
00:00
Est. 1 min
Marks:
+1.00
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Passage
Let
W
=
{
A
∈
R
2
×
2
:
A
=
−
A
T
}
W=\{A\in\mathbb{R}^{2\times2}:A=-A^T\}
. Based on the above data, answer the given subquestions.
Question
Which of the following sets form a basis for
W
W
?
Comprehension
Easy Difficulty
29 October 2023
A
S
=
{
[
1
0
0
0
]
,
[
0
0
0
1
]
,
[
0
1
−
1
0
]
}
S=\left\{\begin{bmatrix}1&0\\0&0\end{bmatrix},\begin{bmatrix}0&0\\0&1\end{bmatrix},\begin{bmatrix}0&1\\-1&0\end{bmatrix}\right\}
B
S
=
{
[
0
1
0
0
]
,
[
0
0
−
1
0
]
}
S=\left\{\begin{bmatrix}0&1\\0&0\end{bmatrix},\begin{bmatrix}0&0\\-1&0\end{bmatrix}\right\}
C
S
=
{
[
0
1
−
1
0
]
}
S=\left\{\begin{bmatrix}0&1\\-1&0\end{bmatrix}\right\}
D
S
=
{
[
0
1
0
0
]
,
[
0
0
1
0
]
}
S=\left\{\begin{bmatrix}0&1\\0&0\end{bmatrix},\begin{bmatrix}0&0\\1&0\end{bmatrix}\right\}
