Solving a system of linear equations using Cramer's rule
Cramer's rule may only be applied for a system of linear equations with as many equations as unknowns (the coefficient matrix of the system must be square) and with non-zero determinant of the coefficient matrix.
Consider a system of n linear equations for n unknowns x1
, ..., xn
+ ...+ a1n
+ ...+ a2n
... ... ... ... ...
+ ...+ ann
The determinant of the coefficient matrix
be the determinant of the matrix formed by replacing the j column with the column of the constant terms
, the system has a unique solution
Since the computation of large determinants is cumbersome, Cramer's rule is generally used for systems of two and three equations.