# Math Help - Is the rank of a 3x3 matrix all 0 .....

1. ## Is 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?

2. It is 0 since there are no nonzero rows after row reduction.

3. Another way of seeing it: The rank of a matrix from $R^m$ to $R^m$ is the dimension of the subspace it maps $R^n$ into. The 0 matrix maps every vector into the 0 vector- a "subspace" of dimension 0.