Could there be only one lower and one upper triangle?

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annoyinggirl
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I'm doing LU factorization in linear algebra.

And in general, do i know that i got the right one, given that there are many ways to get the desired entries into zeros, but results in different upper and special lower triangles?
 
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What do you mean with "the right one"? Without further requirements (e.g. "L has diagonal entries that are all 1") the solution is not unique, but every solution should work then. If some further step has additional requirements, you have to identify them.
 
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