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## Homework Statement

Hi, I am really having trouble with questions regarding proving whether a given set is a vector space or not.

So one of the questions is [ x ε R

^{2}|x

_{1}

^{2}=x

_{2}

^{3}]

So I have to prove whether the following set is a vector space

## Homework Equations

## The Attempt at a Solution

Having a peek at the textbook, it tells me that there are ten axioms that satisfy whether a set belongs to a vector space.

What I did was go x

_{1}

^{2}- x

_{2}

^{3}= 0

u+ v = v + u -For this one, I did the following: I let x1 and x2 have a value each and named it a vector u, then I let x1 and x2 have some other values and named it a vector v.

So x1 = 1 and x2 = 2 and u = 1

^{2}- 2

^{3 }

And x1 = 4 and x2 = 5 and v = 4

^{2}- 5

^{3}

u + v = v + u should work out and I used the same method for the rest of the axioms....I need to know two things

(a) Is the method I am doing correct? If not, could you point me in the right direction?

(b) How do I go about checking the first axiom for the above set u + v lies in the set. If I do the same old substitution, all i get is a number, whatever it is!

Thanks