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.
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