Question 10 - Week 3 Practice | Prasnya
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Week 3
Question 10
00:00
Est. 2 min
Marks:
+4.00
0.00
Passage
Suppose
W
1
W_1
and
W
2
W_2
are subspaces of
R
3
\mathbb{R}^3
defined as follows:
W
1
=
{
(
0
,
y
,
z
)
∣
y
,
z
∈
R
}
,
W
2
=
{
(
x
,
y
,
z
)
∈
R
3
∣
x
+
y
+
z
=
0
}
,
W_1=\{(0,y,z)\mid y,z\in\mathbb{R}\},\quad W_2=\{(x,y,z)\in\mathbb{R}^3\mid x+y+z=0\},
with usual addition and scalar multiplication. Based on the above data, answer the given subquestions.
Question
Which of the following options represents
W
1
∩
W
2
W_1\cap W_2
? One or more options may be correct.
Comprehension
Medium Difficulty
23 February 2025
A
{
α
(
0
,
1
,
−
1
)
+
β
(
0
,
−
1
,
1
)
∣
α
,
β
∈
R
}
\{\alpha(0,1,-1)+\beta(0,-1,1)\mid \alpha,\beta\in\mathbb{R}\}
B
Span
{
(
0
,
1
,
−
1
)
,
(
0
,
−
1
,
−
1
)
}
\operatorname{Span}\{(0,1,-1),(0,-1,-1)\}
C
Span
{
(
0
,
1
,
−
1
)
}
\operatorname{Span}\{(0,1,-1)\}
D
{
α
(
2
,
−
1
,
−
1
)
+
β
(
0
,
1
,
1
)
∣
α
,
β
∈
R
}
\{\alpha(2,-1,-1)+\beta(0,1,1)\mid \alpha,\beta\in\mathbb{R}\}
