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Math Help - subspaces

  1. #1
    Junior Member
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    Question subspaces

    Hi,

    How can I show that th set of all solutions to Ax = b where A is mxn, is not a subspace of R^n if b <> 0.

    If Ax = 0, (b = 0), the set of solutions IS a subspace. What difference does it make whether b is 0 or not?

    Thanks!
    Last edited by CaptainBlack; November 3rd 2008 at 02:57 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by kpizle View Post
    Hi,

    How can I show that th set of all solutions to Ax = b where A is mxn, is not a subspace of R^n if b <> 0.

    If Ax = 0, (b = 0), the set of solutions IS a subspace. What difference does it make whether b is 0 or not?

    Thanks!

    EDIT: Moving question to more appropriate forum
    Suppose x is a solution to this and \lambda is a scalar, then A(\lambda x)=\lambda b, so \lambda x is not in the set of solutions unless b=0, but if the set of solutions is a subspace it would have to be.

    CB
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