8. Abstract Vector Spaces and Subspaces

Verifying Vector Space Axioms In Context — Quiz

Test your understanding of verifying vector space axioms in context with 5 practice questions.

Practice Questions

Question 1

Which vector space axiom says that for every vector $v$, there is a vector $-v$ such that $v+(-v)=0$?

Question 2

Suppose a set of vectors is closed under addition, but multiplying a vector by $-1$ can produce a vector outside the set. Which axiom fails?

Question 3

In any vector space, the equation $v+0=v$ describes which axiom?

Question 4

Which property is expressed by $u+v=v+u$ for all vectors $u$ and $v$?

Question 5

For all scalars $a$ and $b$ and vector $v$, the equation $(a+b)v=av+bv$ is an example of which axiom?