Is the rank of a 3x3 matrix with 0 for all entries 0 or 3?

0 Isnt it? (Wondering)

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- Jul 26th 2010, 11:08 AMadam_leedsIs the rank of a 3x3 matrix all 0 .....
Is the rank of a 3x3 matrix with 0 for all entries 0 or 3?

0 Isnt it? (Wondering) - Jul 26th 2010, 11:15 AMlvleph
It is 0 since there are no nonzero rows after row reduction.

- Jul 27th 2010, 04:40 AMHallsofIvy
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.