Cramer's method is useful for instructive purposes, and also for
theory, but practically, it is highly inefficient.  The method used by
SymPy is Gaussian elimination, which is the most direct way to solve a
system of linear equations.

Of course, if you want to use SymPy to use Cramer's method, that is
possible.  I'm not sure what the best method to get the matrices with
columns replaced is.  Perhaps we should add some method like
col_replace (and row_replace) to Matrix, which would make this easier.

Aaron Meurer

On Thu, Aug 30, 2012 at 2:06 PM, Sachin Joglekar
<srjoglekar...@gmail.com> wrote:
> I am new to Sympy and started using it recently. I just have a doubt that
> can we use Determinants and Crammers law to solve first degree simultaneous
> equations using sympy? will it be faster/slower than the current
> implementation in the module?
>
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