> 
> **Question:**
>  Let $\vec u,\vec v$ and $\vec w$ be vectors in $\Bbb R^n$. Suppose that $\vec u,\vec v, \vec w$ are linearly independent. Show that $\vec u+\vec v$, $\vec u-3\vec w$ and $2\vec v-3\vec w$ are linearly independent. 
> 
> 
> 

I understand that if a vectors are linear independent if the equation 

$$a\_1\vec v\_1 + a\_2\vec v\_2 + \cdots + a\_k\vec v\_k = 0$$

so when 
$$a\_1 = a\_2 = \cdots= a\_k = 0.$$

I just don't understand how to explain, any help would be appreciated, thanks guys!