Prove that if $ u \cdot v = u \cdot w $ then $v = w$ I've tried putting it up as:
$$ [u_1 v_1 + \ldots + u_n v_n] = [u_1 w_1 + \ldots + u_n w_n] $$
But this doesn't make it immediately clear...I can't simply divide by $u_1 + \ldots + u_n$ as these ($u$, $v$ and $w$) are vectors...
Any hints?

Can I not choose $u=(1,0,0)$, $u=(0,1,0)$ and $u=(0,0,1)$. When I plug them into $u\cdot v=u\cdot w$, I get three equations: $v_1=w_1$, $v_2=w_2$ and $v_3=w_3$, so $v$ must be equal to $w$. 
