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Math Help - Vector Subspaces

  1. #1
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    Vector Subspaces

    Are the following vector subspaces??
    X= (x \in Q^4: x_1+x_2-x_3-x_4=x_1+x_4=0)

    and

     X=(x\in Q^4: x_1^2+x_2^2-x_3^2-x_4^2=0)

    I don't think the second one is (under addition x+y) but i'm not sure
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by cassius View Post
    Are the following vector subspaces??
    X= (x \in Q^4: x_1+x_2-x_3-x_4=x_1+x_4=0)

    and

     X=(x\in Q^4: x_1^2+x_2^2-x_3^2-x_4^2=0)

    I don't think the second one is (under addition x+y) but i'm not sure
    Why do you think so? Let's see some reasoning?
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  3. #3
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    hi!
    I thought if we take Y\in Q^4... then  (x_1+y_1)^2 is not the same as   x_1^2+y_1^2 etc...
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by cassius View Post
    hi!
    I thought if we take Y\in Q^4... then  (x_1+y_1)^2 is not the same as   x_1^2+y_1^2 etc...
    Hmm, I'm not quite sure what you mean by this?
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  5. #5
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    Quote Originally Posted by Drexel28 View Post
    Hmm, I'm not quite sure what you mean by this?
    i'm sorry my friend confused me with this, she might have had transformations in mind

    I know that for a subspace, if x and y are in the subspace then so is x+y
    " " " x multiplied by scalar
    " " " zero element
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