I want to do LU decomposition with $A$:
$ A= \left[ {\begin{array}{cc} 1 & 2 & 3 & 4 \\ -9 & 8 & -15 & 4 \\ 2 & 13 & -21 & 7 \\ 4 & -5 & 5 & 3 \end{array} } \right] $
My answer is this, which the result is approximation because of limitations of floating point data. $A$ can be done LU decomposition without pivoting.
But WolframAlpha gives me different solution. They do LU decomposition with pivoting. I don't know why WolframAlpha calculate LU decomposition with pivoting even pivoting isn't needed.