Thanks! I did my best to report the bug.  
http://code.google.com/p/sympy/issues/detail?id=3321&sort=-id&colspec=ID%20Type%20Status%20Priority%20Milestone%20Reporter%20Summary%20Stars

On Friday, July 6, 2012 3:55:39 PM UTC-4, Aaron Meurer wrote:
>
> On Thu, Jul 5, 2012 at 7:48 PM, Chris Smith <[email protected]> wrote: 
> > On Thu, Jul 5, 2012 at 5:56 PM, Andrew <[email protected]> wrote: 
> >> Hi, I am very new to sympy and python, so pardon my simple question 
> >> 
> >> I have a matrix right here like this (4 equations, 3 unknowns) 
> >> mat1= 
> >> [   0,    15.0, 10.0, 700.0] 
> >> [   1,    1,      1,     100.0] 
> >> [   0,    10.0,  5.0,  200.0] 
> >> [-5.0,    0,      0,     0] 
> >> 
> >> and a list of unknowns 
> >> unknown=[y0,y1,y2] 
> >> 
> > 
> > Which columns do those variables correspond to? If you multiply the 
> > matrix by a length-4 column vector of variables and pass this to solve 
> > it gives 
>
> I think the way solve_linear_system is supposed to work is that the 
> last column represents the right hand side of the equation.  So a row 
> [1, 2, 3, 4] would represent 1*x1 + 2*x2 + 3*x3 = 4.  In other words, 
> it's an augmented matrix. 
>
> > 
> >>>> v = var('a:d') 
> >>>> v 
> > (a, b, c, d) 
> >>>> v = Matrix([list(v)]).T 
> >>>> e=m*v 
> >>>> solve(e) 
> > {c: -160.0*d, b: 60.0*d, a: 0} 
> > 
> > And the determinant of the matrix is 0: 
> > 
> >>>> m.det() 
> > 0 
>
> I don't think that the determinant has anything to do with it. 
>
> The row [1, 1, 1, 100] clearly corresponds to the solution given. 
>
> The problem seems to have something to do with using floats.  If you 
> do mat1 = mat1.applyfunc(Integer), you get the correct solution.  The 
> problem also exists when using mat1.rref().  This is clearly a bug. 
> Can you report it at code.google.com/p/sympy/issues/list? 
>
> Aaron Meurer 
>
> > 
> > So it looks like there are infinite solutions. I don't spend much time 
> > working with the individual solver routines, so I'm not sure how you 
> > should pass the variables, but perhaps you can start by reading the 
> > docstring (help(solve_linear_system)) where you will see that you 
> > should be passing an augmented system. I don't think you are doing 
> > that. 
> > 
> > /c 
> > 
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