Question: Object too large : Determinant of a large matrix

I'm attempting to solve a system of 47 equations (for 47 unknowns) analytically via matrix methods.  My equations can be written as the product of a 47x47 matrix of coefficients and a 47 row column vector of variables.  I'm trying to find the determinant of the 47x47 matrix of coefficients.

I've done this succesfully for simpler systems (or around 20 equations) however when I try to use the same method for this larger system I get the error (after a few minutes of computation)

"Error, (in LinearAlgebra:-Determinant) object too large"

The equations are not that complicted, I don't see why maple is struggling, I know collegues who solve 6000x6000 matrices!  Is there a way to get around this error -maple isn't coming close to using all of the available memory on my system.