We can explore homogeneous systems easily in Sage with commands we have already learned. Notably, the zero_vector() constructor will quickly create the necessary vector of constants (Sage V).
You could try defining a function to accept a matrix as input, augment the matrix with a zero vector having the right number of entries, and then return the reduced row-echelon form of the augmented matrix, or maybe you could return the number of free variables. (See Sage RCLS for a refresher on how to do this). It is also interesting to see how .solve_right() behaves on homogeneous systems, since in particular we know it will never give us an error. (Why not? Hint: Theorem HSC.)