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(LinearAlgebra) If a vector space is given, how do I know if W is subspace or not?

  1. Aug 4, 2011 #1
    1. The problem statement, all variables and given/known data

    Let V be the spcae of all 3x3 matrices with real entries. Is W, the set of all 3x3 lower triangular matrices, a subspace of V? Why or why not?


    2. Relevant equations



    3. The attempt at a solution


    I just think that all 3x3 lower triangular matrices are included in all 3x3 matrices with real entires.
    So my answer is that W is a subspace of V. but I don't know correct answer.
    and I don't know how to explain why I think W is a subspace of V...
    I think I'm missing an important definition or theorem...?
     
  2. jcsd
  3. Aug 4, 2011 #2

    vela

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    Re: (LinearAlgebra) If a vector space is given, how do I know if W is subspace or not

    That just means W is a subset of V.
    You're missing the definition of a subspace. You need to understand that first. Then there's a theorem that tells you what you need to show to prove W is a subspace of V.
     
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