Of all knowledge, apart from mathematics and demonstrative logic, they consist of conjectures [6].In plausible reasoning, conjecture is the name given to the proposition that is formed from indications and observations, that is, from experience through induction.In mathematics, the concept of conjecture refers to a statement that is supposed to be true, but has not yet been proven or disproved.Once the veracity of a conjecture is demonstrated, it will be considered a theorem.This research shows how to do mathematics by first making conjectures through non-routine problems of linear algebra.