Solving Ag=b with non symmetric A
Maybe this helps. One method to do this is to use least squares (as was mentioned by @cc7768).
Matlab does this by default when using the \ operator.
This is also useful because it's sensible even if the system is overidentified as in the following example:

A = [1 22; 2 100; 7 6]
b = [1 2 5]'
A\b


produces

ans =

    0.7108
    0.0061


. In Python, this can be done with

import numpy
from numpy import linalg
A = numpy.matrix("1 22; 2 100; 7 6")
b = numpy.matrix("1 2 5").T
linalg.lstsq(A,b)[0]


which gives

matrix([[ 0.71084144],
        [ 0.00611577]])


.