Question 9 - Week 4 Practice | Prasnya
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Week 4
Question 9
00:00
Est. 2 min
Marks:
+3.00
0.00
Which of the following is a basis for
V
=
{
A
∈
M
2
×
2
(
R
)
∣
A
T
=
A
}
V=\{A\in M_{2\times2}(\mathbb{R})\mid A^T=A\}
, the vector space of
2
×
2
2\times2
real symmetric matrices?
Single correct
Medium Difficulty
13 July 2025
A
{
[
0
1
1
0
]
,
[
0
0
0
1
]
,
[
1
0
0
0
]
,
[
1
0
0
1
]
}
\left\{\begin{bmatrix}0&1\\1&0\end{bmatrix},\begin{bmatrix}0&0\\0&1\end{bmatrix},\begin{bmatrix}1&0\\0&0\end{bmatrix},\begin{bmatrix}1&0\\0&1\end{bmatrix}\right\}
B
{
[
0
1
1
0
]
,
[
1
0
0
1
]
}
\left\{\begin{bmatrix}0&1\\1&0\end{bmatrix},\begin{bmatrix}1&0\\0&1\end{bmatrix}\right\}
C
{
[
0
1
1
0
]
,
[
0
0
0
1
]
,
[
1
0
0
0
]
}
\left\{\begin{bmatrix}0&1\\1&0\end{bmatrix},\begin{bmatrix}0&0\\0&1\end{bmatrix},\begin{bmatrix}1&0\\0&0\end{bmatrix}\right\}
D
{
[
1
0
0
1
]
,
[
1
0
0
0
]
,
[
0
0
0
1
]
}
\left\{\begin{bmatrix}1&0\\0&1\end{bmatrix},\begin{bmatrix}1&0\\0&0\end{bmatrix},\begin{bmatrix}0&0\\0&1\end{bmatrix}\right\}
