I am having trouble proving the following...

Let B be a basis for a finite dimensional inner product space V.

Prove that <x,z>=0 implies x=0 (the zero vector) for all z in B.

Also prove that <x,z>=<y,z> implies x=y for all z in B.

So far all I have is proof that at least one element of z must be nonzero, hence one element of x is zero, cant get any farther though.

Any help would be appreciated.

Thanks