1. Definition
If det(A)≠0, the unique solution of Ax=b is xᵢ = det(Aᵢ)/det(A), where Aᵢ replaces column i by b.
2. Symbols
| Symbol | Meaning |
|---|
| Aᵢ | A with column i replaced by b |
| det(A) | coefficient determinant |
| xᵢ | i-th unknown |
3. How this tool works
- Cramer's rule requires det A≠0 and a square system;
- Compute one determinant per column replacement;
- An n×n system needs n+1 determinants; inefficient for large n.
4. Steps
- Enter A and b;
- Click Calculate to see det(A) and det(Aᵢ);
- Read each xᵢ.
5. Example
Example: A=2 1;1 −1, b=1 2. det=−3, x₁=1, x₂=−1.
6. Pitfalls
Cannot use it when det A=0;
Only for square systems with equal equations and unknowns;
Prefer Gaussian elimination for large n.