
Linear Combinations and Span in Linear Algebra

Interactive Video
•
Mathematics
•
9th - 12th Grade
•
Hard
Standards-aligned

Emma Peterson
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a linear combination in the context of vectors?
A sum of vectors scaled by arbitrary constants
A product of vectors
A vector multiplied by itself
A vector divided by a constant
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example given, what is the result of 3 times vector a plus minus 2 times vector b?
Vector 0, 0
Vector 3, 0
Vector 1, 2
Vector 0, 3
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the term 'linear' used in linear combinations?
Because vectors are squared
Because vectors are added and scaled, not multiplied by each other
Because vectors are multiplied by each other
Because vectors are divided by constants
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the span of two vectors a and b represent?
The set of all vectors that can be formed by multiplying a and b
The set of all vectors that can be formed by adding and scaling a and b
The set of all vectors that can be formed by dividing a and b
The set of all vectors that can be formed by subtracting a and b
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Can any two vectors always span R2?
No, not all pairs of vectors can span R2
No, only collinear vectors can span R2
No, only orthogonal vectors can span R2
Yes, any two vectors can span R2
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the span of the zero vector?
All vectors in Rn
All vectors in R3
Only the zero vector
All vectors in R2
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is required for two vectors to span all of R2?
They must be identical
They must be parallel
They must be orthogonal
They must be collinear
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