(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The set of all pairs of real numbers of the form (1,x) with the operations:

(1,x)+(1,y)=(1,x+y) and k(1,x)=(1,kx) k being a scalar

Is this a vector space?

2. Relevant equations

(1,x)+(1,y)=(1,x+y) and k(1,x)=(1,kx)

3. The attempt at a solution

I verified most of the axioms hold, but I'm unsure about the additive identity.

Can it be something other than the zero vector?

My attempt, "O" being the additive identity

O=(1,0)

A+O=(1,x)+(1,0)=(1,x)

This means the additive inverse must equal (1,0)

A+(-A)=(1,x)+(-1,-x)=(1,x+(-x))=(1,0)

If this isn't right, then I know it doesn't hold. I'm just a little confused. Thanks for any help

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# Determining if certain sets are vector spaces

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