I thought I could prove this using numbers, but my professor says not to so I'm not exactly sure how else I can prove this.

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

(a) Prove that if <x,z> = 0 for all z in B, then x = 0.

(b) Prove that if <x,z> = <y,z> for all z in B, then x = y.

It seems like an easy problem, but I just can't figure it out. Thanks!