linearly independent elements of W I want to ask about the number of linearly independant elements of 
$W=(u_{1},u_{2},...,u_{m},u_{1}-u_{2},u_{2}-u_{3},...,u_{m-1}-u_{m},u_{m}-u_{1})$.
I say that it is $m$ and i need someone to confirm or not that.
Thanks 

Note that:
$$u_{1}-u_{2},u_{2}-u_{3},...,u_{m-1}-u_{m},u_{m}-u_{1}$$
are linerly dependent by
$$u_{1},u_{2},...,u_{m}$$
thus the number of linearly independant elements of $W$ is equal to the number of linearly independant elements among $u_{1},u_{2},...,u_{m}$.
