Solve Ax=b with LU factorization

I'm trying to solve A*x = b with LU decomposition and back substitution. Where x is the unknown vector.

A =

   350      0     0     0     0
    -1      0     0     0     0.0091
     5      0     0     0     0
     0.0095 0     0     0     1
     0     -1     0     0     0.0091

b =

     1     
     0    
     2   
     1

But I always end up with: Matrix is singular to working precision

Hope someone can provide me with a working code.

Answer 1

[John D'Errico]

The matrix is singular! Hint: read the error message. There is no solution.

Worse, there could NEVER be a solution, even if the matrix was not singular!!!!!!!

A is a 5x5 matrix. b is a 4x1 vector.

There exists no possible vector x such that A*x will be a 4x1 vector. NOT gonna happen. EVER. So asking for working code to do the impossible is a waste of CPU cycles. Trying to do that with a singular matrix? Even sillier.