Mathematica is a great computer algebra system to use, especially if you are in applied areas where it is necessary to solve differential equations and other complicated problems. It was created by a brilliant entrepreneur, who inspired by Maxima, the first computer algebra system in the world, produced an elegant, coherent, and extremely general approach to computing. Mathematica provides friendly tools to solve and plot solutions of many problems, but it is certainly not a panacea of all issues. This computer algebra system has tremendous plotting capabilities. There is a free version of Mathematica featuring its syntax and functions---Mathics that was developed by a team led by Jan Pöschko. It is backed by highly extensible Python code, relying on SymPy for most mathematical tasks. Mathics is released under the GNU General Public License (GPL).
A solution of a realistic problem is often hampered because the algebra is too complex for anyone but the dedicated researcher. Just as the calculator eliminated laborious numerical computations, symbolic software programs eliminate arduous algebraic computations. While computer power is no substitute for thinking, it spares the scientist from performing mundane mathematical steps, and thereby frees time for creative thinking. This tutorial can be used to introduce students who are taking the first course in Linear Algebra to a symbolic mathematical computation program Mathematica that was conceived by a theoretical physicist Stephen Wolfram (born in 1959 in London, England) in late 1980's.