Question

Is Crammer’s Rule always applicable when trying to solve a system of linear equations? Explain.

Answer 1

No. It's not always applicable.
The system must have the same number of equations as variables, that is, the coefficient matrix of the system must be square.

Answer 2

No, Crammer’s Rule isn’t always applicable when trying to solve a system of linear equations because let’s say for example, if the determinant of the coefficient matrix is 0, then Cramer's rule cannot be applied. This usually happens there’s no solution or an infinite number of solutions. In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.