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Math Help - Subspace for R^3

  1. #1
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    Subspace for R^3

    {(x1, x2, x3)^T | x3 = x1 or x3 = x2}

    I know it is not a subspace of R^3, however I'm not exactly sure why. I'm thinking it is because of the OR in the statement? In an earlier problem I had to prove that the same set and statement x1 = x2 = x3 is a subspace, which held true. But this OR is throwing me off. Any ideas?
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  2. #2
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    Quote Originally Posted by pakman View Post
    {(x1, x2, x3)^T | x3 = x1 or x3 = x2}

    I know it is not a subspace of R^3, however I'm not exactly sure why. I'm thinking it is because of the OR in the statement? In an earlier problem I had to prove that the same set and statement x1 = x2 = x3 is a subspace, which held true. But this OR is throwing me off. Any ideas?
    This is not a subspace it is not closed

    Example

    consider v_1=(1,2,1) \mbox{ and } v_2=(-1,-2,-2)

    both v_1,v_2 fit the above criteria but

    v_1+v_2=(1,2,1)+(-1,-2,-2)=(0,0,-1)

    This is not in the "subspace" because x_3=-1

    but both x_1 \mbox{ and } x_2=0

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