Cramer's rule: for Ax=b, xᵢ = det(Aᵢ)/det(A) where Aᵢ replaces column i with b. Requires det(A) ≠ 0 (unique solution). If det(A) = 0: no solution or infinite solutions. Works for any n×n system but is practical for small systems.
How to Use
Enter the system:
- Coefficients: Matrix entries
- Constants: Right-hand side
- Output: Solutions x, y, (z)
Method
- Compute D = det(A)
- Replace column 1 → Dx
- Replace column 2 → Dy
- x = Dx/D, y = Dy/D
When It Fails
D = 0 means no unique solution. The system is either inconsistent (parallel lines) or dependent (same line). Use row reduction instead.
Step-by-Step Instructions
- 1Choose 2×2 or 3×3.
- 2Enter coefficients.
- 3Enter constants.
- 4View determinants.
- 5Get solution.