Question 24 - Week 3 Practice | Prasnya
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Week 3
Question 24
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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
W
1
=
{
(
x
,
y
,
x
−
2
y
)
:
x
,
y
∈
R
}
W_1=\{(x,y,x-2y):x,y\in\mathbb{R}\}
and
W
2
=
{
(
x
,
0
,
y
)
:
x
,
y
∈
R
}
W_2=\{(x,0,y):x,y\in\mathbb{R}\}
with usual addition and scalar multiplication. Answer the given subquestions.
Question
Which of the following options is true?
Comprehension
Easy Difficulty
16 October 2022
A
W
1
∪
W
2
W_1\cup W_2
is a vector space of dimension
3
3
with usual addition and scalar multiplication.
B
W
1
∪
W
2
W_1\cup W_2
is a vector space of dimension
2
2
with usual addition and scalar multiplication.
C
W
1
∪
W
2
W_1\cup W_2
is a vector space of dimension
1
1
with usual addition and scalar multiplication.
D
W
1
∪
W
2
W_1\cup W_2
is not a vector space with usual addition and scalar multiplication.