Vector Spaces

I am struggling with the following question. I need to redefine a vector space in such a way that only four axioms are required. I think I have the four identified as follows:
1. u + v is in V
2. u + 0 = u
3. u + -u = 0
4. cu is in V

Am I in the ball park here at all. I would appreciate any help

thanks

Quote:

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Originally Posted by kdynamos

I am struggling with the following question. I need to redefine a vector space in such a way that only four axioms are required. I think I have the four identified as follows:
1. u + v is in V
2. u + 0 = u
3. u + -u = 0
4. cu is in V

Am I in the ball park here at all. I would appreciate any help

thanks

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I think you need to replace 3) by . This is very important...