GNU Octave
GNU Octave
See also maxima.sourceforge.io
This was my go to software for experimenting with linear algebra etc. Haven’t had the need recently though.
Maxima is a fairly complete computer algebra system written in Lisp with an emphasis on symbolic computation. It is based on DOE-MACSYMA and licensed under the GPL free software license. Its abilities include symbolic integration, 3D plotting and solving differential equations.