For symbolic computations using linear algebra, polynomials, and basic calculus, the system called PARI/GP is very useful. This system is free, open-source, and should be installed on students workstations. User guides can be viewed at the PARI/GP website: http://pari.math.u-bordeaux.fr

The following files contain examples for using pari to do linear algebra:
Pari examples of Matrix Multiplication (text version).
Pari examples of Linear Systems (text version).
Pari examples of Gauss-Jordan Elimination (text version).
Pari examples of Homogeneous systems of curve coefficients (text version).
Pari examples of Matrix Inverses (text version).
Pari examples of Cramer's Rule (text version).


Matt Klassen