
Understanding Basis and Dimension in Vector Spaces

Interactive Video
•
Mathematics
•
10th Grade - University
•
Hard

Emma Peterson
FREE Resource
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a necessary condition for a set to span a subspace V?
It must contain only zero vectors.
It must have at least as many elements as any basis of V.
It must be linearly dependent.
It must have fewer elements than any basis of V.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the thought experiment, what is the significance of adding a vector from the basis to the set B?
It makes the set linearly independent.
It ensures the set no longer spans V.
It demonstrates that the set is linearly dependent.
It reduces the number of elements in the set.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens when a basis vector is added to a set that already spans V?
The set becomes a basis for V.
The set remains linearly dependent.
The set becomes linearly independent.
The set loses its ability to span V.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the outcome of the thought experiment regarding the spanning set B?
B can have fewer elements than the basis and still span V.
B must have at least as many elements as the basis to span V.
B becomes a basis for V.
B is linearly independent.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why can't a spanning set have fewer elements than a basis?
Because it would not include zero vectors.
Because it would make the set linearly independent.
Because it would contradict the definition of a basis.
Because it would increase the dimension of the space.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of replacing elements in a spanning set with basis elements?
The set becomes a basis for the vector space.
The set remains a spanning set.
The set no longer spans the vector space.
The set becomes linearly independent.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the dimension of a vector space defined?
As the number of zero vectors in the space.
As the number of spanning sets in the space.
As the number of elements in any basis of the space.
As the number of linearly dependent vectors in the space.
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