ASAP

The set that this vector space is based on is standard ordered pairs but the operations are nonstandard. So you will have to go through all the axioms if you think it is a vector space or find one that fails and demonstrate it fails with a numeric example.

Do your own work. Copying off of someone else will be useless practice for the exam question.

To prove V is a vector space is a formal proof. There is freedom in styles of presentation but each of the 10 axioms must be justified. All parts require that you start by identifying where/what your variables represent. So normally start:

Proof
Given x,y,z objects in set V and alpha, betta real numbers then…..
Axiom 1: x+y =……. this is in the set V because…… (make sure you check that it is the right type and that it has the properties of any extra conditions you have)
Axiom 2: x+y=……..=y+x (this is prove an identity start with one side go to other)
.
.
.
Conclusion:
QED

Order matters! Must prove commutative first or other axioms become more complicated. Must prove existence of additive identity before additive inverse.
Make sure justify in set of what you claim is the zero vector not just that the equation is satisfied.
Make sure justify in set of what you claim is the additive inverse not just that the equation is satisfied.

When check closure make sure that you

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