@Swati GATE does have a syllabus http://syllabus.gatecse.in
There was a big change in this in 2016 where many portions were removed. These questions are tagged "non-gate" or "out-of-syllabus" here.
LU decomposition added here in Linear Algebra from Numerical methods which was removed as a whole otherwise.
http://gatecse.in/gate-cse-2016-syllabus/
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Gatecse
X->YZ , Y->XZ , ...