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Question 9 - Week 4 Practice | Prasnya
Q9
00:00
13 Jul 2025
Q9.
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\}
V
=
{
A
∈
M
2
×
2
(
R
)
∣
A
T
=
A
}
, the vector space of
2
×
2
2\times2
2
×
2
real symmetric matrices?
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\}
{
[
0
1
1
0
]
,
[
0
0
0
1
]
,
[
1
0
0
0
]
,
[
1
0
0
1
]
}
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\}
{
[
0
1
1
0
]
,
[
1
0
0
1
]
}
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\}
{
[
0
1
1
0
]
,
[
0
0
0
1
]
,
[
1
0
0
0
]
}
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\}
{
[
1
0
0
1
]
,
[
1
0
0
0
]
,
[
0
0
0
1
]
}
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Q9
00:00
13 Jul 2025
Q9.
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\}
V
=
{
A
∈
M
2
×
2
(
R
)
∣
A
T
=
A
}
, the vector space of
2
×
2
2\times2
2
×
2
real symmetric matrices?
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\}
{
[
0
1
1
0
]
,
[
0
0
0
1
]
,
[
1
0
0
0
]
,
[
1
0
0
1
]
}
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\}
{
[
0
1
1
0
]
,
[
1
0
0
1
]
}
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\}
{
[
0
1
1
0
]
,
[
0
0
0
1
]
,
[
1
0
0
0
]
}
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\}
{
[
1
0
0
1
]
,
[
1
0
0
0
]
,
[
0
0
0
1
]
}
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