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Math Help - Dealing with

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    7

    Dealing with

    Let W be a subspace of Kn and

    v is also contained in Kn<br />

    Need to determine if v is contained in W<br /> <br />
    v =

    3
    1
    2
    3

    W = rowspace(A)

    A =

    2411
    3402
    1212

    over

    According to the notes we will find another matrix B where:

    W = nullspace(B)<br />
    Then after GJ A =<br />
    1004
    0100
    0013

    And then aparantlly

    From this information you can get a single bias vector
    =
    1
    0
    2
    1

    But i dont see how??

    Any help would be great
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  2. #2
    MHF Contributor

    Joined
    Apr 2005
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    I wouldn't worry about finding this "B". The definition of "row space of A" is the space spanned by the rows of A. In order to prove that < 3 1 2 3> is in that rwo space, you must show that it can be written as a linear combination of rows of A: that is, find a, b, c such that a<2 4 1 1>+ b<3 4 0 2>+ c<1 2 1 2>= <3 1 2 3>. That is the same as showing that it is possible to solve 2a+ 3b+ c= 3, 4a+ 4b+ 2c= 1, a+ c= 2, and a+ 2b+ 2c= 3.
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