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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.

46 votes

Why linear algebra is fun!(or ?)

My favorite elementary application of linear algebra is proving that the decomposition used in Calculus of rational functions into partial fractions works. Start with a polynomial $Q(x)=(x-r_1)(x-r_2 …