Question

v=vector space over R. show that it is a vector space. explain me a little

Answer 1

http://en.wikipedia.org/wiki/Euclidean_space

Answer 2

A vector space holds 8 properties:
\[\forall a,b,v_1,v_2,v_3 \in X\]
\[v_1+(v_2+v_3)=(v_1+v_2)+v_3\]
\[v_1+v_2=v_2+v_1\]
There exists a zero element denoted 0 such that:
\[v+0=v; \forall v \in X\]
There exists a negative element denoted -v such that:
\[v+(-v)=0\]
\[a(v_1+v_2)=av_1+av_2\]
\[(v_1+v_2)a=av_1+av_2\]
\[(ab)v_1=a(bv_1)\]
There exists an identity element e. Such that:
\[e(v_1)=v_1\]