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Matrix elimination


Dear comunity,
I'm trying to play around with the simple matrixes in Mathematica for the first time and I have beginners question:

Does Mathematica have a function, which makes the intermediate step of Gaussian elimination to produce just eliminated upper triangular matrix? Function UpperTriangular only cuts the lower triangular places off (which is not what I need) and RowReduce makes the completely reduced echelon form of matrix. 
I needed the step in the middle of the RowReduce way.

Thanks in advance for any tips

Jakub



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