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Math Help - Row Space Proof

  1. #1
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    Row Space Proof

    Let A be an mxn matrix with entries in F. Let Row(A) be a subset of M1xn(F) be the span of the rows of A.
    Let
    P Mmm(F) be an mm matrix. Show that Row(PA) Row(A), with equality of P is invertible.

    Last edited by amm345; November 3rd 2009 at 10:23 PM.
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  2. #2
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    The row space of a matrix is orthogonal to the null space of that matrix. If P is invertible, PAv= 0 if and only if Av= 0. That is, the null space of PA is the same as the null space of A and so the row spaces are also the same.
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