We could compute the column space of a matrix with a span of the set of columns of the matrix, much as we did back in Sage CSS when we were checking consistency of linear systems using spans of the set of columns of a coefficent matrix. However, Sage provides a convenient matrix method to construct this same span: .column_space(). Here is a check.
In Sage CSS we discussed solutions to systems of equations and the membership of the vector of constants in the span of the columns of the coefficient matrix. This discussion turned on Theorem SLSLC. We can now be slightly more efficient with Theorem CSCS, while still using the same ideas. We recycle the computations from Example CSMCS that use Archetype D and Archetype E.