Question 11 - Week 3 Practice | Prasnya
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Week 3
Question 11
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Est. 1 min
Marks:
+2.00
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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 option is true?
Comprehension
Easy Difficulty
23 February 2025
A
W
1
∪
W
2
W_1\cup W_2
is a subspace of dimension
3
3
.
B
W
1
∪
W
2
W_1\cup W_2
is a subspace of dimension
2
2
.
C
W
1
∪
W
2
W_1\cup W_2
is a subspace of dimension
1
1
.
D
W
1
∪
W
2
W_1\cup W_2
is not a subspace.