Does the Vector Space Axiom Hold for V with Given Conditions?

[Rigid@motion]

let V be the collection of the 2*3 matrices with a real entries such that
V={[a11 a12 a13 : a21 a22 a23] | a11+a23 =1}
determine whether the following vector space axioms holds
(a) for all α ε V there exists (-α) such that α + (-α)=0(vector)

 

[Rigid@motion]

let V be the collection of the 2*3 matrices with a real entries such that
V={[a11 a12 a13 : a21 a22 a23] | a11+a23 =1}
determine whether the following vector space axioms holds
(a) for all α ε V there exists (-α) such that α + (-α)=0(vector)

please help

 

[HallsofIvy]

Wow! You waited a whole 12 minutes before "bumping"! I would think that when you read through the information that you had to say you had read when you registered here, you would have seen that bumping, even after days, is prohibited and can get you barred.

Also in those same documents you said you read, you are told that anything that looks like school work or homework- which this certainly is- you must make an attempt to do the problem yourself and show your work.

I will move this the homework section and give you 24 hours to post what you have tried on this yourself. If you have not put anything up by that time, I will delete this thread.

(If you know the definitions of "0 vector" and "additive inverse" ("negative") of a vector, this problem should be easy. If you don't know those definitions, the first thing you should have done was look them up.)