Matrix Builder
Legend & Hints
Highlighted cell shows current pivot for that step.
Input accepts integers, fractions like 3/7, or decimals.
Enable augmented mode to classify solution type via ranks.
Export results and full step log.
Results
pivot per step
Enter a matrix and click Compute RREF to see steps.
Example Data Table
Classic 3×4 augmented system example:
| 1 | 2 | -1 | 8 |
|---|---|---|---|
| -3 | -1 | 2 | -11 |
| -2 | 1 | 2 | -3 |
Formula Used
- Elementary row operations: swap Ri ↔ Rj, scale Ri ← k·Ri (k≠0), add multiple Rr ← Rr − a·Ri.
- Pivot selection: partial pivoting chooses the largest-magnitude nonzero entry in the current column to improve numerical stability.
- Gauss–Jordan: For each pivot column, scale the pivot row to make pivot 1, then eliminate above and below to produce zeros.
- RREF conditions: nonzero rows above zero rows; pivot of each nonzero row equals 1; each pivot is the only nonzero in its column; pivots move strictly rightward.
- Rank and consistency: With augmented matrices, compare rank(A) and rank([A|b]). If unequal, system is inconsistent. If equal and less than variables, infinitely many solutions; if equal to variables, unique solution.
How to Use
- Choose matrix dimensions. Enable augmented mode if solving a system.
- Enter entries as integers, fractions like
7/4, or decimals. - Click Compute RREF. Each step shows the operation and pivot.
- Switch display between fractions and decimals, choose decimal precision.
- Download your steps and final matrix as CSV or PDF.
FAQs
Up to 10×10 matrices. Larger sizes may be unwieldy on small screens.
Yes. Fractions are handled symbolically to avoid round‑off. You can switch to decimals for readability.
Partial pivoting picks the largest magnitude in the column below the active row, then swaps rows before scaling.
Yes. In augmented mode, ranks are compared. If rank(A) differs from rank([A|b]), the system is inconsistent.
When rank is less than variables, there are free variables. The count equals variables minus rank.
Exact elimination can temporarily increase numerator and denominator sizes. Switch to decimals for a compact view.