#### analytic linear system solving (27.11.97)

Forwarded from Olivier Froment SNCF - Ecole Centrale de Paris

I would like to solve symbolically a linear system of the (classical ) form : Ax=b

where A is ”almost ”full 6*6 square matrix

Up to 5, that seems possible but with 6 the objects manipulated seem too large...

Is there something I can do for simplifying , before solving the system, the shape of matrix A to make it
work?

I once had a verb—16x16— matrix to deal with, and I found using the LU factorization to be very
helpful.

By coincidence I also recently wanted a symbolic solution for an ”almost” full 6*6 square matrix. Mine
solved, but took a long time to produce a very large and awkward solution. In the end I found the LU
decomposition much more useful (command linalg[LUdecomp](...)).

In fact it was fairly easy to apply an LU decomposition such as Crout’s algorithm (Numerical Recipes in
C, W.H. Press et al. (1992)) manually to the matrix.