  This paper outlines our ideas on how to teach linear algebra in a mechanized
mathematical environment, and discusses some of our reasons for thinking that
this is a better way to teach linear algebra than the ``old fashioned way''. We
discuss some technological tools such as Maple, Matlab, Python, and Jupyter
Notebooks, and some choices of topics that are especially suited to teaching
with these tools. The discussion is informed by our experience over the past
thirty or more years teaching at various levels, especially at the University
of Western Ontario.
