A=matrix(QQ,[[ 1, 1, 0, -1, -1 ],
[ 0, 1, 1, -1, 1 ],
[ 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 2 ]])
A.LU()
results in U not in row echelon form
'SageMath Version 7.0, Release Date: 2016-01-19'
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