Does Cramers Rule Work

Cramer’s Rule is a viable and efficient method for finding solutions to systems with an arbitrary number of unknowns, provided that we have the same number of equations as unknowns. … To find out if the system is inconsistent or dependent, another method, such as elimination, will have to be used.

Does Cramers rule always work?

Cramer’s Rule only works on square matrices that have a non-zero determinant and a unique solution.

How do you know if Cramer's rule is not applicable?

Use Cramer’s rule to efficiently determine solutions to linear systems. When the determinant of the coefficient matrix is 0, Cramer’s rule does not apply; the system will either be dependent or inconsistent.