The question:

Prove that the following properties are true for every vector space.

a) 2v=v+v

b)nv=v+ ... +v, where there arenterms on the right

My attempt:

a) Letvbe an element of vector space $\displaystyle V^n$.

2v= $\displaystyle 2\begin{pmatrix} x_1 \\ x_2 \\ ...\\ x_n \end{pmatrix}$ = $\displaystyle \begin{pmatrix} 2x_1 \\ 2x_2 \\ ...\\ 2x_n \end{pmatrix}$

v + v = $\displaystyle \begin{pmatrix} x_1 \\ x_2 \\ ...\\ x_n \end{pmatrix}$ + $\displaystyle \begin{pmatrix} x_1 \\ x_2 \\ ...\\ x_n \end{pmatrix}$ = $\displaystyle \begin{pmatrix} 2x_1 \\ 2x_2 \\ ...\\ 2x_n \end{pmatrix}$

Therefore 2v=v+v

Is this correct, or am I approaching this the wrong way? Thanks!