How to find the basis of a matrix with variables?

I give up after hours of reading in the documentation of MuPAD.

Simple question is already in the title. Here is my matrix:

A:=matrix([[1,a,a,1],[1,1,3,b],[1,b,4,1],[1,b,5,1]]);

I really hope it is possible.

linalg::basis did not work for me, because it needs a set or list of vectors. I created vectors then:

v1 := matrix([1,1,1,1]): v2 := matrix([a,1,b,b]): v3 := matrix([a,3,4,5]): v4 := matrix([1,b,1,1]):

linalg::basis([v1,v2,v3,v4])

Still does not work. Please help me.