Is the rank of a 3x3 matrix with 0 for all entries 0 or 3? 0 Isnt it?
Last edited by mr fantastic; Jul 27th 2010 at 04:56 AM. Reason: Copied title into main body of post, minor consequential editing.
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It is 0 since there are no nonzero rows after row reduction.
Another way of seeing it: The rank of a matrix from $\displaystyle R^m$ to $\displaystyle R^m$ is the dimension of the subspace it maps $\displaystyle R^n$ into. The 0 matrix maps every vector into the 0 vector- a "subspace" of dimension 0.
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