public static double[] LinSolve(double[,] A, double[] b, out bool isValid)
{
var rref = A.AppendColumn(b).ReducedRowEchelonForm();
var rows = rref.GetLength(0);
var cols = rref.GetLength(1);
isValid = true;
const double Tolerance = 1e-12;
for (int row = 0; row < rows; row++)
{
for (int col = 0; col < cols - 1; col++)
{
var value = rref[row, col];
if (row == col)
{
if ((value - 1).Abs() > Tolerance)
{
isValid = false;
break;
}
}
else
{
if (value.Abs() > Tolerance)
{
isValid = false;
break;
}
}
}
}
return(rref.GetColumn(rref.GetLength(1) - 1));
}