Ti-83 Calculator... Matrices with polynomial coefficients..?

Is there a program for the ti-83 that can solve systems of equations with polynomial coefficients? Or anyway to create and manipulate matrices that contain polynomial coefficients?

I am using Cramer's rule to solve systems of differential equations in Laplace space. So, almost all of the coefficients contain an unknown complex number 's'. With 3 or more equations, this becomes rather cumbersome to do by hand.

Yes, this can easily be done in Mathematica or Matlab, but I can only use a Ti-83.