I'm given that $\begin{align*} u &= (1, 2, 3)\\ v &= (2, -1, 1)\\ w &= (3, 1, 0) \end{align*}$
And I'm asked to verify if $\langle x,u\rangle = \langle x, v\rangle = \langle x,w\rangle = 0$ then $x=0$
I'm not really sure where to start. Logically, isn't it obvious? I know the following: $\begin{align*} \langle x, u\rangle &= x_{1} + 2x_{2} + 3x_{3}.\\ \langle x, v\rangle &= 2x_{1} - x_{2} + x_{3}\\ \langle x, w\rangle &= 3x_{1} + x_{2} \end{align*}$
But does that get me any where? I feel like I should be thinking about linearly independence and the matrix:
$\begin{bmatrix} 1 & 2 & 3\\ 2 & -1 & 1\\ 3 & 1 & 0 \end{bmatrix}$
Could someone point me in the right direction?