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Why is it not possible for the columns of a matrix to span R^2 even if

  1. Oct 14, 2012 #1
    Why is it not possible for the columns of a matrix to span R^2 even if those columns do not span R^3?
     
  2. jcsd
  3. Oct 14, 2012 #2

    Bacle2

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    Re: Span

    You may end up with a rank-1 matrix after row-reduction.
     
  4. Oct 14, 2012 #3

    HallsofIvy

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    Re: Span

    Is that really what you meant to ask? There is no "why" for a statement that isn't true to begin with! The columns of the matrix
    [tex]\begin{bmatrix}1 & 1 & 0 \\ 1 & -1 & 0 \\ 0 & 0 & 0\end{bmatrix}[/tex]
    do span R2 but not R3.

    (Bacle answered a different question: Why is it possible that the columns of a matrix do not span R2?)
     
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