I am using solve() to solve a system of equations. Fortunately, the system is linear. Since it has more than 700 variables and more than 300 equations, I actually don't know if the solution exists.
I called solve() to solve the problem, and the solution I got indicates that all the variables are free variables. (That is, the solution is given as x_k = x_k for all variables.) Obviously, my system is not homogeneous, and 0 is not a solution to my problem. (I plugged in 0 and verified it.)
Since all the coefficients to my system are fractions, so I suppose the solve() function is using some symbolic algorithms? I don't know why this happens. Does this mean there is no solution to my system?