1. Let V be a vector space over a field F, and $\displaystyle v_1, v_2,...,v_n \in V$. If there is an i>1 such that $\displaystyle v_i \in span(v_1, v_2,...,v_{i-1})$, then $\displaystyle span(v_1,...,v_n)=span(v_1,...,v_{i-1},v_{i+1},...,v_n)$.

I'm not sure how to start this problem. I don't know what properties to apply to this problem.

2. Let V be a vector space over a field F, and $\displaystyle v_1, v_2,...,v_n \in V$. Let $\displaystyle u_i = v_i-a_i v_1$, where $\displaystyle a_i \in F$ and $\displaystyle 2\leq i \leq n$. Show that if $\displaystyle u_2,...,u_n$ are linearly dependent, then $\displaystyle v_1,...,v_n$ are also linearly dependent.