  In this paper, we investigate the importance of column scaling in relating
two signed-graphic representations of the same matroid. We used the Sage
Mathematics software to generate many examples of signed-graphic matroids and
their signed-graphic representations. Our examples show that column scaling is
sometimes necessary in order to transform one signed-graphic representation
into another; moreover, there exist many collections of signed-graphic
representations that row-reduce to the same standard form. We also discuss an
interesting matroid-preserving operation on a signed graph, which we call the
cylinder flip, that relates certain pairs of signed-graphic representations of
the same matroid.
