Question

The vector space which has only the additive Identity element zero is

Answer 1

Step-by-step explanation:

Looking at the various axioms for vector spaces, I'm getting hung up on this one:

Additive Identity

The set V contains an additive identity element, denoted by 0, such that for any vector v in V, 0+v=v and v+0=v.

It seems simple enough but in an example given -

V={⎡⎣⎢1+x2−x3+2x⎤⎦⎥∣∣∣x∈R}

And the additive identity is -

0=⎡⎣⎢123⎤⎦⎥

I'm confused by this as certainly, v+0≠v.

I'd appreciate any help in understanding this, thanks