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Math Help - linear Algebra- Inner products

  1. #1
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    Red face 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!
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  2. #2
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    Quote Originally Posted by mathgirl View Post
    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).
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