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Math Help - solutions

  1. #1
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    solutions

    i dont really understand this statement. can someone explain to me?

    what does it mean:

    Ax=b has solutions iff APy=b has solutions.

    in my notes, it states that that means that column operations dont change the span of the columns...but i still dont get what that means
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    The statement is true in general for P invertible.

    In fact, if x_0 is a solution of Ax=b then

    AP(P^{-1}x_0)=Ax_0=b

    This implies that y_0=P^{-1}x_0 is a solution for APy=b

    It's easy to prove the reciproque.

    Regards

    ---
    Fernando Revilla
    Last edited by FernandoRevilla; November 11th 2010 at 05:20 AM.
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