Just started learning it and didn't quite get the hang of it.

So here are the questions:

Let V be an inner product space and $\displaystyle U,W \subseteq{V}$ prove that:

1. a. Solved nvm this one

b. Solved nvm this one

c. $\displaystyle V=U\oplus{W} \Leftrightarrow V=U^\bot \oplus {W^\bot}$

2.In inner product space V we are given {$\displaystyle v_1,....,v_k$} vectors for which

$\displaystyle \|{v}\|^2=(v,v_1)^2+.....+(v,v_k)^2$.

Show that V=span{$\displaystyle v_1,....,v_k$}

Thanks for any help in advance.