Question 22 - Week 4 Practice | Prasnya
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Week 4
Question 22
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Est. 2 min
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Choose all the correct options from the following.
Multiple correct
Medium Difficulty
27 October 2024
A
For a vector space
V
V
with dimension
n
n
, there is always a subspace of dimension
k
k
where
1
≤
k
<
n
1\le k<n
.
B
Let
S
S
be a set of
k
k
vectors in
R
n
\mathbb{R}^n
. Then
span
(
S
)
\operatorname{span}(S)
has dimension less than or equal to
k
k
.
C
Let
S
S
be a subset of a vector space
V
V
of dimension
n
n
. Then
S
S
can have a maximum of
n
n
linearly independent vectors.
D
A finite non-empty set of vectors from a vector space can never be a subspace.
