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

fackert
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Why is it not possible for the columns of a matrix to span R^2 even if those columns do not span R^3?
 
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You may end up with a rank-1 matrix after row-reduction.
 


fackert said:
Why is it not possible for the columns of a matrix to span R^2 even if those columns do not span R^3?
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
\begin{bmatrix}1 & 1 & 0 \\ 1 & -1 & 0 \\ 0 & 0 & 0\end{bmatrix}
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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