SingularMatrixException when solving Linear EquationSystem

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I use EJML to solve a linear equation system.

EJML uses doubles. My inputs (and expected outputs) are integers. I will omit the .000 from the toString().

My Matrix A looks like this (though it is ~1000x1000):

1  0  0  0  0
1 -1  1  0  0
0  1 -1  1  0
0  0  1 -1  1
0  0  0  0  1

My b is just a vector with a value in the first and the last index, the rest is 0.

{-10 0 0 0 10}'

For size 5x5 I can use EJML just fine, but for my 1000x1000 Matrix I get a Solution contains uncountable numbers-Error.

The result looks like this:

{NaN NaN NaN ... NaN -Infinity -Infinity 1}'

My code looks like this (the matrices are correct, I checked that via Sysout and Debugger):

// Setup A
// Setup b
SimpleMatrix x = A.solve(b);

Now I assume my System somehow behaves badly. Sadly I'm not that much into matrices, so I assume I'm maybe using the wrong methods to solve this particular problem. The other thing I can think of is that double-precision gets in my way.

Is there anything I can do or is EJML simply not the right tool here?

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