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Homework Help: Vector Free spaces

  1. Mar 11, 2012 #1
    1. The problem statement, all variables and given/known data
    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

    3. 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
  2. jcsd
  3. Mar 11, 2012 #2
    You want to consider the closeness of this set under arbitrary linear combination, including zero vector, etc.
  4. Mar 11, 2012 #3
    you mean axioms for a free space?
  5. Mar 11, 2012 #4
    I meant axiom for a vector space (closeness under linear combination), if that's not what you meant, ignore what I said.
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