Reduced Row Echelon Form for Specified Rank

I have a very ill-conditioned matrix A that I know has theoretical rank . I want to convert this mtarix to reduced row echelon form, but because of the ill conditioning of this matrix, too many rows are set to zero by the rref MATLAB built-in. I believe that this has to do with the ill-conditioning of the problem. How do I enforce a condition on the rank of A when using the rref built-in?

Thank you!

[Sharmin Kibria]

Hi Sam,

rref accepts a tolerance option. Maybe you can try changing the tolerance value in rref to ensure the rows are not set to zeros.

https://www.mathworks.com/help/matlab/ref/rref.html?searchHighlight=rref&s_tid=srchtitle#d123e1181996