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the cramers rule is applied on matrices
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The matrices that follow d rule of reflexivity is known as ref matrix
Unless your "everyday life" involves work in some area of engineering, you won't use matrices in your everyday life.
In math, the purpose of Cramer's rule is to be able to find the solution of a system of linear equations by using determinants and matrices. Cramer's rule makes it easy to find a system of equations that have many unknown variables.