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Math Help - Prove that T is a subspace in R^n

  1. #1
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    Prove that T is a subspace in R^n

    T = { x E R^n | x . v = 0 for all v E S } ____________[E means 'element of']

    "Let S be a subspace of of R^n and let that is, T is the set of all vectors in R^n that are orthogonal to every vector in S."

    thank you, so how do i go about this what are the steps?

    thanks again
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  2. #2
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    Re: Prove that T is a subspace in R^n

    You just have to show that all the axioms hold for all vectors in T

    Vector space - Wikipedia, the free encyclopedia
    Thanks from Jesssa
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    MHF Contributor FernandoRevilla's Avatar
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    Re: Prove that T is a subspace in R^n

    Quote Originally Posted by Brennox View Post
    thank you, so how do i go about this what are the steps?
    According to a well known theorem you have to prove: (i) 0\in T. (ii) For all x,y\in T, x+y\in T. (iii) For all \lambda\in\mathbb{R} and for all x\in T, \lambda x\in T. Try to prove those properties.
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