"The system cannot be solved: the matrix is singular or close to singular." in LU decomposition

Question

Hello,

I have a problem using sho LU decompusition from C# code. 

When I do 

var solver = new LU(leftPart);
var x = solver.Solve(rightPart);

the exception "The system cannot be solved: the matrix is singular or close to singular." is thrown in the Solve method invokation. The leftPart is invertible. The determenant is 22142.9

When I do 

solver.PermMatrix.Inv()*solver.L*solver.U 

I get the leftPart. Thats why I can say the decomposition itself works correctly. But the invokation of Solve method doesn't work.

When I do manual computaion instead of calling Solve method like

var x = solver.U.Inv()*solver.L.Inv()*solver.PermMatrix*rightPart;

I get the result and no exception is thrown. The solution exists.

So please tell me what is is problem? Is this a bug? Or I use LU object incorrectly?

the leftPart is

[ 1,0000            1,0000          1,0000          0,0000    0,0000    0,0000
  51,9300           53,4300         31,7800         0,0000    0,0000    0,0000
 -10,2500           -6,2500         35,2200         0,0000    0,0000    0,0000
  153336928,2251    137718739,3027  0,0000          35,2200   31,7800   1,0000
  577859,9901       0,0000          137718739,3027  -6,2500   53,4300   1,0000
  0,0000            577859,990      153336928,2251  -10,2500  51,9300   1,0000]

the right part is 

  [ 0,0000
  0,0000
  0,0000
  19,5129
  9,8517
  10,6909]

Thanks, Dmitry.