Gauss Elimination and LU Decomposition

If I apply normal Gaussian Elimination to find L and U matrices, I tend to end up with an incorrect solution set [x1 x2 x3](Transposed) in the end. I have checked all the n-1 steps of normal GE very carefully. I don't see what I did wrong there. I think it's probably due to bad rounding off errors.

If anyone knows what I did wrong, please tell me. thanks.