
Understanding Vector Spaces and Basis

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

Mia Campbell
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What are the two conditions for a set of vectors to be considered a basis for a vector space?
The set must be dependent and span the space.
The set must be independent and span the space.
The set must be independent and not span the space.
The set must be dependent and not span the space.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you determine if a set of vectors is independent?
By checking if the vector equation has only the trivial solution.
By checking if the vectors can be written as a linear combination.
By checking if the vector equation has non-trivial solutions.
By checking if the vectors are orthogonal.
Tags
CCSS.8.EE.C.8B
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does it mean if a vector equation has non-trivial solutions?
The set of vectors spans the space.
The set of vectors is dependent.
The set of vectors does not span the space.
The set of vectors is independent.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the next step after identifying a dependent set of vectors?
Solve the vector equation again.
Eliminate vectors corresponding to free variables.
Add more vectors to the set.
Eliminate vectors corresponding to basic variables.
Tags
CCSS.8.EE.C.8B
CCSS.HSA.REI.C.6
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of setting up an augmented matrix for the system of equations?
To find the determinant of the matrix.
To solve for the basic and free variables.
To check if the vectors are orthogonal.
To determine if the set spans the space.
Tags
CCSS.8.EE.C.8B
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What form is the augmented matrix written in to identify the basic and free variables?
Row echelon form
Reduced row echelon form
Identity form
Diagonal form
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which variables are considered basic variables in the reduced row echelon form?
Variables corresponding to the first non-zero entries in each row.
Variables that are zero in the matrix.
Variables corresponding to the last non-zero entries in each row.
All variables in the matrix.
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