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Math Help - subspace proof help

  1. #1
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    subspace proof help

    V is any vector space,  U = W_{1}       U      W_{2} where  W_{1} , W_{2} are subspace of V.

    Prove U is not a subspace of the vector space V.
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  2. #2
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    Re: subspace proof help

    For example, let us consider two subspaces S & T of the vector space R3 where S = {(x,y,z) : y=0 , z=0} T = {(x,y,z) : x=0, z=0}
    let a=(1,0,0) belongs to S & b=(0,1,0) belongs to T. But a+b does not belong to SUT
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  3. #3
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    Re: subspace proof help

    You can't prove this, It isn't true unless you have restrictions on W_1 and W_2. For example, if the vector space is R^3, W_1= \{x, y, 0\}, and W_2= \{x, 0, 0\} then W_1\cap W_2= W_2which certainly is a subspace.

    What is true is that W_1\cap W_2 is a subspace if and only if one is a subspace of the other.

    In order to prove this, you will have to make use of the fact, which isn't true unless one is NOT a subspace of the other, that there exist a vector u in W_1 that is not in W_2 and that there exist a vector v in W_2 that is not in W_1.
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