Linear Combinations of Vectors

Quiz
•
Mathematics
•
12th Grade
•
Hard
Anthony Clark
Used 1+ times
FREE Resource
13 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Option (a)
Option (b)
Option (c)
Option (d)
2.
FILL IN THE BLANK QUESTION
1 min • 1 pt
The linear span L(S) of any subset S of a vector space V(F) is a .........of V(F).
3.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
In a vector space of dimension 5, a subset A containing 6 elements is generating set. Then
A is Linearly independent also.
There is one element in A which can be written as a linear combination of others.
A contains zero element
Can not say anything about the set A
4.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
If W is a subspace of a vector space V(F) and α, β ∈ W then for any scalar c ..........
cα + β ∈ V
cα + β ∈ W
cα + β ∉ V
cα + β ∉ W
5.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Is the vectors (1, 2, 3), (4, 5, 6) and (7, 8, 9) span the vector
space ℝ3.
yes
no
6.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Let V be a vector space, and let W be a subset of V. What does it mean when we say that is linearly independent?
S is closed under both addition and scalar multiplication.
The only way to write 0 as a linear combination of elements of S.
All the elements of are distinct from each other.
S has nullity zero.
7.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Let V be a five-dimensional vector space, and let S be a subset of V which spans V . Then S
Must have exactly five elements.
Must consist of at least five elements.
Must have infinitely many elements.
Must have at most five elements.
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