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Math Help - subspace test

  1. #1
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    subspace test

    Let A be an nn matrix and let W = {v ∈ Rn|Av = 2v} . Is W a subspace of Rn?
    I don't know how to prove it using the subspace test.


    I know that W is a subspace of Rn.

    I tried saying that the 0 vector is a element of W since v is a element of Rn. Av = 2v

    How do you do the addition and scalar multiplication?

    Never mind.. I figured it out.
    Last edited by yangx; November 13th 2012 at 10:11 PM.
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  2. #2
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    Re: subspace test

    all you have to do is verify closure under vector addition and scalar multiplication (since you've already covered the additional requirement that 0 is in W).

    so suppose u,v are in W. is u+v in W? if c is any scalar (real number, in this case), is cu in W?
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