We do not assign problems which need
computer algebra software (CAS) in this course.
Nevertheless, it is useful to know what can
be done with such programs like
"the four M's". With CAS it is
like with driving cars, if you know one of them, you know
to use them all...
We recommend you do all the homework without CAS, but
it is certainly allowed (even recommended) to use one of
these tools to check your work.
Below are some
Mathematica,
Matlab or
Maple and
Maxima
commands for linear algebra. The code speaks for itself.

Mathematica

Harvard has a Mathematica site license. You can
get it here
and request a password,
using the Harvard Site License Number L2482-2405.

Maxima is an open
source CAS originally developed by the
DOE.
While having less features than the commercial CAS, it is
GPL'd
and free software: you can
see the code.
(echelon(A) is here an upper
triangular matrix);