Vector Space Quiz

Which of the following is a vector in R3?

• [12]

• [3−25]

• [01]

• [1234]

A vector space must be closed under which two operations?

• Differentiation and integration

• Multiplication and division

• Vector addition and scalar multiplication

• Transposition and inversion

Which one is NOT a property of a vector space?

• Associative multiplication

• Distributive scalar multiplication

• Additive inverse

• Zero vector exists

The zero vector in any vector space:

• Does not exist

• Depends on the scalar

• Is the additive identity

• Must have all components as one

The set of all vectors in R2 is a:

• Matrix

• Subspace

• Vector space

• Scalar field

If v=[2−1], then 3v=?

• [6−3]

• [50]

• [3−3]

• [61]

If a set is closed under addition but not under scalar multiplication, is it a vector space?

• Yes

• No

Which of the following is not required for a subspace?

• Contains zero vector

• Closed under scalar multiplication

• Nonlinear transformation

• Closed under addition

A subspace must always pass through:

• The origin

• A scalar

• A plane

• A random point

Which of the following sets is a subspace of R2?

• Set of all vectors with first component 1

• Set of all zero vectors

• Set of all vectors with second component 1

• Set of all non-zero vectors