Understand the subject
What does solving Ax=b mean?
A linear system asks which vector x the matrix A sends to the target vector b.
Use it to distinguish unique, infinite, and inconsistent solution sets.
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
Ax=b
Interpret with care
Important boundary
A solution classification depends on pivots in the augmented matrix, not only the number of equations.
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
[A|b] → RREF
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
A pivot in every variable column gives a unique solution; free variables give infinitely many.
[A|b] → RREF
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.
