Question 4 - Week 3 Practice | Prasnya
Prasnya
Continue with Google
Practice path
Dashboard
Exam
Qualifier / Quiz 1
Go to subject
Mathematics 2
Go to chapter
Week 3
Question 4
00:00
Est. 3 min
Marks:
+6.00
0.00
Choose all the correct statements from the following.
Multiple correct
Medium Difficulty
26 October 2025
A
The set of positive real numbers is a vector subspace of
R
\mathbb{R}
with the standard addition and multiplication.
B
In any vector space
V
V
, if for some
c
∈
R
c\in\mathbb{R}
and
v
∈
V
v\in V
, we have
c
⋅
v
=
0
c\cdot v=0
, then
c
=
0
c=0
or
v
v
is the zero vector.
C
If a vector subspace of
R
3
\mathbb{R}^3
with usual addition and scalar multiplication contains finitely many elements, then it is the trivial subspace, i.e., the subspace with only the zero vector.
D
Any subset of a spanning set of a vector space is a spanning set.
E
Any subset of a linearly independent set in a vector space is a linearly independent set.
