while learning from tutorial, I was able to understand first paragraph clearly. I can also see that we just need to find out elementary cycles in graph(which can be done with how to find primary cycles in undirected graph ? , an answer written by Aditya Prakash) .

Now I am not able to grasp how does gaussian method works. I have also tried to look into some solutions like, born2rule , rajat1603 , shubhamgoyal__ . all this solutions look very similar, which uses gaussian method.

so , can someone help me out with gaussian method ? what it actually does ? and when can we use it ?