\enspace The system of linear equations has to be converted into and augmented matrix. Steps to follow when using Cramers rule linear algebra:Ģ. Still Cramers rule is an important piece of linear algebra to be considered due its mathematical rigor and the deep understanding of the transcription of linear systems into matrices, and viceversa, when such systems have unique solutions.īut what is Cramers rule perse? Instead of reciting a Cramers rule definition, let us showcase the technique a little better by going through its steps in detail.
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The reason for it is that Cramers rule is not practical when a system is of higher order than 3, other methods, such as solving a linear system with matrices using Gaussian elimination, or simply solving systems of linear equations by substitution are much more computationally effective to work through a linear system. Throughout this lesson we will focus on explaining the method for solving a system that we will call Cramers rule 3x3 and Cramers rule 2x2, this means that we will focus on the cases where we have a system of equations with 3 equations for 3 unknowns (n=3) or a system with 2 equations for 2 unknowns (n=2). The technique consists on a set of equations involving determinants and ratios in order to obtain the unique set of solutions for a linear system.
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Solving linear systems using Cramers RuleĬramers rule is a technique to solve systems of linear equations where there are the same amount of unknowns as equations in the system.