Thread: 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?

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

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