Quiz: Linear Algebra - Vector Properties

Master linear algebra vector properties faster - reinforce what you learned in just 5 minutes.

Mathematics mixed 5 Questions Video Quiz

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Q1 Beginner 1 pts

According to the video, what are the two components that comprise a vector in R2? Video Reference:
"this is a vector that just has two coordinates some some x coordinate and some y coordinate right wh..."

Timestamp: 2:00

An x-coordinate and a y-coordinate A magnitude and a direction A scalar and a vector An additive inverse and a zero vector

Q2 Intermediate 2 pts

The video demonstrates that vector addition is commutative, meaning: Video Reference:
"we're seeing that if you instead do you w plus your v you get the exact same thing and so then when ..."

Timestamp: 5:00

v + w = w + v v + (w + u) = (v + w) + u c(v + w) = cv + cw v + (-v) = 0

Q3 Beginner 1 pts

According to the video, scaling a vector v by a scalar c is equivalent to: Video Reference:
"to scale a vector by c you just scale both of its coordinates by c..."

Timestamp: 8:30

Adding c to each coordinate of v Multiplying each coordinate of v by c Raising each coordinate of v to the power of c Dividing each coordinate of v by c

Q4 Intermediate 2 pts

The additive inverse of a vector v is a vector -v such that: Video Reference:
"there exists these kinds of inverses that exist these additive inverses for every vector v there exi..."

Timestamp: 7:30

True

False

Q5 Advanced 3 pts

Which of the following properties of vector addition and scalar multiplication are mentioned in the video? Select all that apply. Video Reference:
"v plus w is w plus v and not only is this in commutative it's also associative excellent associative..."

Timestamp: 6:00

Select all correct answers

Vector addition is commutative Vector addition is associative Scalar multiplication is distributive over vector addition Scalar addition is distributive over vector multiplication

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Quiz: Linear Algebra - Vector Properties

According to the video, what are the two components that comprise a vector in R2? Video Reference: "this is a vector that just has two coordinates some some x coordinate and some y coordinate right wh..." Timestamp: 2:00

The video demonstrates that vector addition is commutative, meaning: Video Reference: "we're seeing that if you instead do you w plus your v you get the exact same thing and so then when ..." Timestamp: 5:00

According to the video, scaling a vector v by a scalar c is equivalent to: Video Reference: "to scale a vector by c you just scale both of its coordinates by c..." Timestamp: 8:30

The additive inverse of a vector v is a vector -v such that: Video Reference: "there exists these kinds of inverses that exist these additive inverses for every vector v there exi..." Timestamp: 7:30

Which of the following properties of vector addition and scalar multiplication are mentioned in the video? Select all that apply. Video Reference: "v plus w is w plus v and not only is this in commutative it's also associative excellent associative..." Timestamp: 6:00