Question 1 - Week 4 Practice | Prasnya
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Week 4
Question 1
00:00
Est. 3 min
Marks:
+4.00
0.00
Consider a subspace
W
=
{
(
x
,
y
,
z
,
w
)
∈
R
4
∣
x
+
y
+
z
=
0
,
y
+
z
=
w
}
W=\{(x,y,z,w)\in\mathbb{R}^4\mid x+y+z=0,\;y+z=w\}
of
R
4
\mathbb{R}^4
. Which of the following options describes a basis of
W
W
?
Single correct
Medium Difficulty
15 March 2026
A
{
(
−
4
,
1
,
3
,
4
)
,
(
0
,
−
5
,
5
,
0
)
}
\{(-4,1,3,4),(0,-5,5,0)\}
B
{
(
1
,
−
1
,
0
,
−
1
)
,
(
0
,
1
,
−
1
,
0
)
,
(
−
1
,
0
,
1
,
1
)
}
\{(1,-1,0,-1),(0,1,-1,0),(-1,0,1,1)\}
C
{
(
−
3
,
1
,
2
,
3
)
,
(
−
1
,
1
,
0
,
1
)
,
(
0
,
−
1
,
1
,
0
)
}
\{(-3,1,2,3),(-1,1,0,1),(0,-1,1,0)\}
D
{
(
0
,
1
2
,
−
1
2
,
0
)
,
(
0
,
−
3
,
3
,
0
)
}
\{(0,\tfrac{1}{2},-\tfrac{1}{2},0),(0,-3,3,0)\}
