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.