calculate the rank of matrix, the matrix contain don't care value( the don't care value can be any number)?

Question

I have a N*M matrix(N is small , but M is large ). The values in the matrix can only be 0, 1, or don't care value(the don't care value can be 0 or 1, denote by Xi). The rank of the matrix depends on the don't care value. I want to calculate the minimum rank of the matrix. The below is a example.

Matrix A :
1 X3 X4
X1 1 X5
X2 X6 1

The matrix A contain don't care value, it can be converted to Matrix A'
1 0 0
1 1 1
0 0 1

and matrix A also can be  converted to matirx A''
1 1 1
1 1 1
1 1 1

the rank of matrix A''  is 1 and the rank of matrix A' is 3, so the minimum rank of the matrix A  is 1.