Understand the subject
What is Cramer’s rule?
Cramer’s rule solves a square nonsingular system by replacing one coefficient column at a time with b.
Use it for small exact systems when determinant structure is the point.
See the structure
What the calculation is doing
[ 1 1 | 3 ]R₂ − 2R₁[ 2 1 | 4 ]→pivots reveal the solution
Worked interpretation
Read the result in context
xᵢ=det(Aᵢ)/det(A)
Interpret with care
Important boundary
It requires a square system and nonzero determinant; it is not a general large-system method.
Use the Matrix Calculator to experiment with small exact matrix operations before applying a more specialized route.
Quick guide
How to use this calculator
- Set the matrix dimensions required by the task.
- Fill every visible entry and any operation-specific control.
- Read the result type, factors, classification, and disclosed limitations.
Calculation method
Apply the stated linear-algebra contract
xᵢ = det(Aᵢ)/det(A)
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
Cramer’s rule requires a square A, one right-hand side, and det(A) ≠ 0.
xᵢ = det(Aᵢ)/det(A)
Supported inputs
Precision and limits
Matrix size
Input matrices are limited to 1–6 rows and columns; operation-specific square, rank, or compatibility rules still apply.
Entry precision
Enter signed finite decimals with at most 30 digits and 15 decimal places.
Exactness
Finite decimals become reduced rational numbers and intermediate structural calculations are not rounded.
