Hi guys.

I need help with the following:

Let $\displaystyle V$ be a vector space over $\displaystyle \mathbb{c}$.

Let $\displaystyle B=\left \{ v_1, v_2,...,v_n \right \}$ be a base for $\displaystyle V$.

a. let $\displaystyle v\in V$ such that for every $\displaystyle i$: $\displaystyle <v_i,v>=0$. prove that $\displaystyle v=0$.

b. let $\displaystyle u,w\in V$ such that for every $\displaystyle i$: $\displaystyle <v_i,u>=<v_i,w>$. prove that $\displaystyle u=w$.

this is what I tried so far:

a.

let $\displaystyle v_j\in B$. since $\displaystyle B$ is base for $\displaystyle V$, then:

$\displaystyle <v_j,v>=<v_j,\sum_{i=1}^{n}\alpha_iv_i>=\overline{ <\sum_{i=1}^{n}\alpha_iv_i,v_j>}=\sum_{i=1}^{n} \alpha_ i \overline{<v_i,v_j>}=...$

not sure what's next, though. what am I missing here?

Am I even in the right direction?

Thanks in advanced!