Cramer's Rule Calculator

Solve a 2x2 or 3x3 linear system Ax = b using Cramer's rule: x_k = det(A_k) / det(A), where A_k is A with column k replaced by b.

Frequently Asked Questions

When does Cramer's rule work?

Whenever the coefficient determinant det(A) is nonzero. If det(A) is zero, the system has no unique solution and Cramer's rule does not apply.

Is Cramer's rule efficient?

For small systems (2x2 or 3x3), yes. For larger systems it is impractical: cofactor expansion grows as n factorial. Gauss-Jordan elimination runs in n cubed.

Does Cramer's rule work for non-square systems?

No. It requires a square invertible coefficient matrix. For non-square systems, use the pseudoinverse or least-squares methods.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.