Basically I have a linear system of equations, where every coefficient is a variable. For example, for a 2x2 system:
- a11*x1 + a12*x2 = f1
- a21*x1 + a22*x2 = f2
x1, x2 = .... (symbolic expression with a11, a12, a21, a22, f1, f2)
I tried solving it in MATLAB via Cramer's rule, writing the matrixes of the system in symbolic form and calculating the appropiate determinants. The issue is, the time required grows very quickly with the size of the system. My problem at hand requires a symbolic solution for a 12x12 system, but the time required with my current code is huge and not likely to finish anytime next month.
What is the best approach to solve this symbolic linear system? Some people told me that Maple is best suited for symbolic operations, could it be significantly faster than MATLAB for calculating symbolic determinants?