# Thread: linear Algebra- Inner products

1. ## linear Algebra- Inner products

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!

2. Originally Posted by mathgirl
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!
(a) Put z=x.
(b) Write it as <x – y, z> = 0 and use (a).