Question 26 - Week 3 Practice | Prasnya
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Week 3
Question 26
00:00
Est. 3 min
Marks:
+4.00
0.00
Which of the following subsets are not vector subspaces of
R
3
\mathbb{R}^3
with respect to usual addition and scalar multiplication? 1)
W
=
{
(
x
,
y
,
z
)
:
x
,
y
,
z
∈
R
,
x
2
=
z
2
}
W=\{(x,y,z):x,y,z\in\mathbb{R},\ x^2=z^2\}
2)
W
=
{
(
x
,
y
,
z
)
:
x
,
y
,
z
∈
R
,
x
=
z
}
W=\{(x,y,z):x,y,z\in\mathbb{R},\ x=z\}
3)
W
=
{
(
x
,
y
,
z
)
:
x
,
y
,
z
∈
R
,
x
=
y
+
z
}
W=\{(x,y,z):x,y,z\in\mathbb{R},\ x=y+z\}
4)
W
=
{
(
x
,
y
,
z
)
:
x
,
y
,
z
∈
R
,
(
x
+
1
)
+
(
y
−
1
)
+
z
=
0
}
W=\{(x,y,z):x,y,z\in\mathbb{R},\ (x+1)+(y-1)+z=0\}
. Enter the serial number of the subset which is not a vector subspace.
Integer answer
Medium Difficulty
05 June 2022
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