It's a question from a test I didn't knew how to solve:
An inner product space in $V=R^n$, such as $\left\langle \pmatrix{ x_1\\ \vdots \\ x_n}\pmatrix{ y_1\\ \vdots\\ y_n} \right\rangle = x_1y_1 + x_2y_2 +\ldots +x_ny_n $ (standard)
$ v , u $ are not linear dependent in $V$. And $W = \operatorname{sp}d \left \{ (u+v),(u-v) \right \}$; now I am asked to prove that if exists a $w$ in $W^\perp$, $w\neq0$ then : $3 \leq \dim(V)$.
I tried to check for dimensions $2$, $1$ and to prove that $w=0$ but with no luck...
Thanks