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Subspace of R^n

  1. Feb 23, 2010 #1
    1. True or False: If U is a subspace of V, and V is a subspace of W, U is a subspace of W.

    If true give proof of answer, if false, give an example disproving the statement.


    2. My thoughts: If U is a subspace of V, then the zero vector is in V. As well as x+v is in V and ax is in V (by definition of a subspace). If these three are in V, and V is in W, then these three must be in W as well. Therefore U will be a subspace of W. However, I don't know if there is an example to disprove this, or if my logic is completely flawed.

    Thanks for any help!
     
  2. jcsd
  3. Feb 24, 2010 #2

    radou

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    U is a subset of V, and V is a subset of W. This implies that U is a subset of W. Since U is closed under addition and scalar multiplication, we conclude...
     
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