Answer
See answer below
Work Step by Step
We are given:
$=$ with $i \in 1,...n$
Thus:
$-=0$
$=0$
Hence, $x-y$ is orthogonal to $v_i$, with $i \in 1,...n$ (1)
According to Gram-Schmidt process, if we have $\{u_1,u_2,...,u_n\}$ we can obtain:
$$v=v+v+...+v$$
Then:
$$u=v+v+...+v=0$$
Since $v=v=...=v$
$u$ is a zero vector. (2)
From (1) and (2), $x-y=0 \rightarrow x=y$
