Vector Space? Determine Axiom Satisfaction

[maiad]

Homework Statement

Determine whether set is a vector space. If not, give at least one axiom that is not satisfied.
the set of vectors <a1, a2> where a2 =3a1+1

The Attempt at a Solution

I'm not sure if this is a vector free space or not,, what I'm confused is about is how the a rule such as "x+y=y+x" can be applied. Would it just be a1 +a2 = a1 +(3a1 +1)=a2+a1=(3a1+1)+a1

 

[sunjin09]

You want to consider the closeness of this set under arbitrary linear combination, including zero vector, etc.

 

[maiad]

you mean axioms for a free space?

 

[sunjin09]

you mean axioms for a free space?

I meant axiom for a vector space (closeness under linear combination), if that's not what you meant, ignore what I said.