What is a necessary condition for a set to be considered a subspace in Rn?

Understanding Subspaces and Transformations

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Mathematics
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11th Grade - University
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Hard

Amelia Wright
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
It must be a finite set.
It must be closed under vector addition and scalar multiplication.
It must contain only positive vectors.
It must contain only integer vectors.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is true about the zero vector in a subspace?
It is not required to be in a subspace.
It must be included in any subspace.
It can be excluded if the subspace is finite.
It is only included if the subspace is infinite.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the image of a subset under a transformation represent?
The subset multiplied by a scalar.
The inverse of the subset.
A new subset in the codomain after transformation.
The original subset in Rn.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens to a triangle in R2 when it is transformed under T?
It remains unchanged.
It becomes a skewed and rotated triangle in the codomain.
It becomes a circle.
It disappears.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can we determine if the image of a subspace V under T is a subspace?
By checking if it is a subset of Rn.
By checking if it contains only positive vectors.
By ensuring it is a finite set.
By verifying closure under addition and scalar multiplication.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the range of a transformation T?
The domain Rn.
The set of all inputs to T.
The set of all possible outputs of T.
The entire codomain Rm.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the image of Rn under T?
It is always equal to Rm.
It represents the range of T.
It is always a subset of Rn.
It is the inverse of T.
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