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Question 4 - Week 3 Practice | Prasnya
Q4
00:00
26 Oct 2025
Q4.
Choose all the correct statements from the following.
A
The set of positive real numbers is a vector subspace of
R
\mathbb{R}
R
with the standard addition and multiplication.
B
In any vector space
V
V
V
, if for some
c
∈
R
c\in\mathbb{R}
c
∈
R
and
v
∈
V
v\in V
v
∈
V
, we have
c
⋅
v
=
0
c\cdot v=0
c
⋅
v
=
0
, then
c
=
0
c=0
c
=
0
or
v
v
v
is the zero vector.
C
If a vector subspace of
R
3
\mathbb{R}^3
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.
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Q4
00:00
26 Oct 2025
Q4.
Choose all the correct statements from the following.
A
The set of positive real numbers is a vector subspace of
R
\mathbb{R}
R
with the standard addition and multiplication.
B
In any vector space
V
V
V
, if for some
c
∈
R
c\in\mathbb{R}
c
∈
R
and
v
∈
V
v\in V
v
∈
V
, we have
c
⋅
v
=
0
c\cdot v=0
c
⋅
v
=
0
, then
c
=
0
c=0
c
=
0
or
v
v
v
is the zero vector.
C
If a vector subspace of
R
3
\mathbb{R}^3
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.
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Check
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