# Thread: Is this a vector space

1. ## Is this a vector space

A = {(x,y)| x,y belong R}
scalar multiplication and addition are defined as
a(x,y) = (ax,ay)
(x1 , y1) + (x2 , y2) = (x1 + x2 + 1, y1+y2+1)

1) can we define zero vector as (-1,-1)
2) can we define -(x,y) as (-x-1,-y-1)
3) is A a vector space

2. ## Re: Is this a vector space

Good questions. Why don't you try answering them?

3. ## Re: Is this a vector space

Your scalar mutiplication must satisfy a(u+ v)= au+ av. Is that true?

yes

5. ## Re: Is this a vector space

I don't see any reason why first and second statements are wrong.
But the theorems -1u = -u and 0u = 0 contradicts my answer.

6. ## Re: Is this a vector space

Originally Posted by HallsofIvy
Your scalar mutiplication must satisfy a(u+ v)= au+ av. Is that true?
Originally Posted by scnakandala
yes