1. The problem is to determine if Cramer's rule can be applied to a given system of linear equations. 2. Cramer's rule applies to a system of $n$ linear equations with $n$ unknowns, represented as $AX = B$, where $A$ is an $n \times n$ coefficient matrix. 3. The key condition for Cramer's rule to apply is that the determinant of matrix $A$, denoted $\det(A)$, must be non-zero: $$\det(A) \neq 0.$$ This ensures the system has a unique solution. 4. If $\det(A) = 0$, Cramer's rule cannot be used because the system either has no solution or infinitely many solutions. 5. To check if Cramer's rule applies, you must: - Write down the coefficient matrix $A$ from the system. - Calculate $\det(A)$. - Verify if $\det(A) \neq 0$. 6. Without the explicit system or matrix $A$, we cannot definitively say if Cramer's rule applies. 7. If you provide the system or matrix, I can help calculate $\det(A)$ and confirm applicability.