Question 4 - Week 5 Practice | Prasnya
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Week 5
Question 4
00:00
Est. 2 min
Marks:
+3.00
0.00
A
A
is a square matrix of order
3
3
. Select all subspaces of
R
3
\mathbb{R}^3
from the options given below.
Multiple correct
Easy Difficulty
07 July 2024
A
S
=
{
v
:
A
v
=
[
0
0
0
]
T
e
x
t
a
n
d
v
∈
R
3
}
S=\{v:Av=\begin{bmatrix}0&0&0\end{bmatrix}^T ext{ and } v\in\mathbb{R}^3\}
B
S
=
{
v
:
A
v
=
[
1
2
3
]
T
e
x
t
a
n
d
v
∈
R
3
}
S=\{v:Av=\begin{bmatrix}1&2&3\end{bmatrix}^T ext{ and } v\in\mathbb{R}^3\}
C
S
=
{
(
x
,
y
)
:
x
,
y
∈
R
}
S=\{(x,y):x,y\in\mathbb{R}\}
D
S
=
{
(
x
,
y
,
0
)
:
x
,
y
∈
R
}
S=\{(x,y,0):x,y\in\mathbb{R}\}
