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Question 1 - Week 3 Practice | Prasnya
Q1
00:00
15 Mar 2026
Q1.
Which of the following subsets are subspaces of
R
3
\mathbb{R}^3
R
3
under the usual addition and scalar multiplication?
A
W
=
{
(
x
,
y
,
z
)
∈
R
3
∣
z
=
2
}
W=\{(x,y,z)\in\mathbb{R}^3\mid z=2\}
W
=
{(
x
,
y
,
z
)
∈
R
3
∣
z
=
2
}
B
W
=
{
(
x
,
y
,
z
)
∈
R
3
∣
x
−
y
+
z
=
0
}
W=\{(x,y,z)\in\mathbb{R}^3\mid x-y+z=0\}
W
=
{(
x
,
y
,
z
)
∈
R
3
∣
x
−
y
+
z
=
0
}
C
W
=
{
(
x
,
y
,
0
)
∣
x
,
y
∈
R
}
W=\{(x,y,0)\mid x,y\in\mathbb{R}\}
W
=
{(
x
,
y
,
0
)
∣
x
,
y
∈
R
}
D
W
=
{
(
x
,
y
,
0
)
∣
x
,
y
∈
R
}
∪
{
(
x
,
y
,
z
)
∈
R
3
∣
x
+
y
+
z
=
0
}
W=\{(x,y,0)\mid x,y\in\mathbb{R}\}\cup\{(x,y,z)\in\mathbb{R}^3\mid x+y+z=0\}
W
=
{(
x
,
y
,
0
)
∣
x
,
y
∈
R
}
∪
{(
x
,
y
,
z
)
∈
R
3
∣
x
+
y
+
z
=
0
}
Save
Check
Details
Q1
00:00
15 Mar 2026
Q1.
Which of the following subsets are subspaces of
R
3
\mathbb{R}^3
R
3
under the usual addition and scalar multiplication?
A
W
=
{
(
x
,
y
,
z
)
∈
R
3
∣
z
=
2
}
W=\{(x,y,z)\in\mathbb{R}^3\mid z=2\}
W
=
{(
x
,
y
,
z
)
∈
R
3
∣
z
=
2
}
B
W
=
{
(
x
,
y
,
z
)
∈
R
3
∣
x
−
y
+
z
=
0
}
W=\{(x,y,z)\in\mathbb{R}^3\mid x-y+z=0\}
W
=
{(
x
,
y
,
z
)
∈
R
3
∣
x
−
y
+
z
=
0
}
C
W
=
{
(
x
,
y
,
0
)
∣
x
,
y
∈
R
}
W=\{(x,y,0)\mid x,y\in\mathbb{R}\}
W
=
{(
x
,
y
,
0
)
∣
x
,
y
∈
R
}
D
W
=
{
(
x
,
y
,
0
)
∣
x
,
y
∈
R
}
∪
{
(
x
,
y
,
z
)
∈
R
3
∣
x
+
y
+
z
=
0
}
W=\{(x,y,0)\mid x,y\in\mathbb{R}\}\cup\{(x,y,z)\in\mathbb{R}^3\mid x+y+z=0\}
W
=
{(
x
,
y
,
0
)
∣
x
,
y
∈
R
}
∪
{(
x
,
y
,
z
)
∈
R
3
∣
x
+
y
+
z
=
0
}
Save
Check
Details
