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Question 11 - Week 6 Practice | Prasnya
Q11
00:00
3 Aug 2025
Q11.
Which of the following spaces are isomorphic to the kernel of
T
T
T
?
@passage
A
The trivial vector space
{
0
}
\{0\}
{
0
}
.
B
The vector space of
2
×
2
2\times2
2
×
2
diagonal matrices.
C
The
y
z
yz
y
z
-plane in
R
3
\mathbb{R}^3
R
3
, i.e.,
{
(
0
,
y
,
z
)
∣
y
,
z
∈
R
}
\{(0,y,z)\mid y,z\in\mathbb{R}\}
{(
0
,
y
,
z
)
∣
y
,
z
∈
R
}
.
D
The vector space of
2
×
2
2\times2
2
×
2
scalar matrices.
E
The space of solutions to
A
x
=
0
Ax=0
A
x
=
0
, where
A
A
A
is an invertible matrix.
F
The
x
x
x
-axis in
R
3
\mathbb{R}^3
R
3
, i.e.,
{
(
x
,
0
,
0
)
∣
x
∈
R
}
\{(x,0,0)\mid x\in\mathbb{R}\}
{(
x
,
0
,
0
)
∣
x
∈
R
}
.
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Q11
00:00
3 Aug 2025
Q11.
Which of the following spaces are isomorphic to the kernel of
T
T
T
?
@passage
A
The trivial vector space
{
0
}
\{0\}
{
0
}
.
B
The vector space of
2
×
2
2\times2
2
×
2
diagonal matrices.
C
The
y
z
yz
y
z
-plane in
R
3
\mathbb{R}^3
R
3
, i.e.,
{
(
0
,
y
,
z
)
∣
y
,
z
∈
R
}
\{(0,y,z)\mid y,z\in\mathbb{R}\}
{(
0
,
y
,
z
)
∣
y
,
z
∈
R
}
.
D
The vector space of
2
×
2
2\times2
2
×
2
scalar matrices.
E
The space of solutions to
A
x
=
0
Ax=0
A
x
=
0
, where
A
A
A
is an invertible matrix.
F
The
x
x
x
-axis in
R
3
\mathbb{R}^3
R
3
, i.e.,
{
(
x
,
0
,
0
)
∣
x
∈
R
}
\{(x,0,0)\mid x\in\mathbb{R}\}
{(
x
,
0
,
0
)
∣
x
∈
R
}
.
Save
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Check
Details
