Let $n\ge 3$ be an integer and let $u_1,u_2,\ldots ,u_n$ be $n$ linearly independent elements in a vector space over $\Bbb R$.Set $u_0=0,u_{n+1}=u_1$.
Define $v_i=u_i+u_{i+1}$ and $w_i=u_{i-1}+u_i$ for $i=1,2,\ldots n$
Then show that $v_1,v_2,\ldots v_n$ and $w_1,w_2,\ldots w_n$ are linearly independent for $n=2011$.
I am unable to understand how to show this for $n=2011$ .Please help.