Issue with lu solver

[Makogan]

I think there's a gotcha situation in which the LU solver fails.

    let decomp = mat.lu();
    let res = decomp.solve(&b).expect(format!("{} {}", mat, b).as_str());

Consider the following linear system:

 ┌                                                                                 ┐
  │          -0           -120.864365                 0           1 │
  │           0           -120.864365                 0           1 │
  │   173502.55     -120.86603   45485.008        1 │
  │           1                            0                      0         0 │
  └                                                                                ┘

 
  ┌   ┐
  │ 0 │
  │ 0 │
  │ 0 │
  │ 0 │
  └   ┘

Since the matrix has a repeated row, there are classes of inputs for which a solution does not exist. However, since it is asking for $b=0$, there is at least one trivial solution of x=0;

I don't know if this is something that wants to be taken into account but I will mention it just in case.