
Understanding Linear Subspaces

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard
Standards-aligned

Sophia Harris
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the definition of Rn in the context of linear algebra?
A set of matrices with n rows
A set of vectors with n components
A set of equations with n variables
A set of scalars with n values
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is NOT a condition for a subset to be a subspace of Rn?
Contains the zero vector
Closed under addition
Closed under scalar multiplication
Closed under vector subtraction
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens when you multiply a vector in a subspace by a scalar?
It becomes the zero vector
It leaves the subspace
It becomes a unit vector
It remains in the subspace
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of subspaces, what does 'closure under addition' mean?
Adding two vectors in the set results in a vector outside the set
Adding a vector and a matrix results in a vector in the set
Adding two vectors in the set results in another vector in the set
Adding a vector and a scalar results in a vector in the set
Tags
CCSS.HSN.VM.A.2
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example of a simple subspace in R3, what is the only vector contained in the set?
The unit vector
The zero vector
The identity vector
A random vector
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the subset S in R2, where x1 is greater than or equal to 0, not a subspace?
It is not closed under scalar multiplication
It is not closed under vector subtraction
It is not closed under addition
It does not contain the zero vector
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the span of a set of vectors represent?
The set of all possible linear combinations of those vectors
The set of all possible scalar multiples of those vectors
The set of all possible additions of those vectors
The set of all possible subtractions of those vectors
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