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3×4 Reduced Row-Echelon Form Calculator — result sheet
Transform a real 3×4 matrix into reduced row-echelon form with partial pivoting, then report rank and pivot columns without interpreting the matrix as a system solution.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Use elementary row operations with scaled partial pivoting to make each pivot 1 and clear its column. The result is the reduced row-echelon form; rank is the number of nonzero pivots and pivot columns are the columns containing those pivots.
Row reduction changes a matrix through reversible elementary row operations while preserving its row-equivalence class. This tool stops at the reduced row-echelon matrix and reports rank/pivot information; it deliberately does not label rows as equations, choose free variables, or return a system-specific solution.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Row 1, column 1 — minimum -1000000; maximum 1000000
- Row 1, column 2 — minimum -1000000; maximum 1000000
- Row 1, column 3 — minimum -1000000; maximum 1000000
- Row 1, column 4 — minimum -1000000; maximum 1000000
- Row 2, column 1 — minimum -1000000; maximum 1000000
- Row 2, column 2 — minimum -1000000; maximum 1000000
- Row 2, column 3 — minimum -1000000; maximum 1000000
- Row 2, column 4 — minimum -1000000; maximum 1000000
- Row 3, column 1 — minimum -1000000; maximum 1000000
- Row 3, column 2 — minimum -1000000; maximum 1000000
- Row 3, column 3 — minimum -1000000; maximum 1000000
- Row 3, column 4 — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Row 1, column 1 | 1 |
| Row 1, column 2 | 2 |
| Row 1, column 3 | 3 |
| Row 1, column 4 | 4 |
| Row 2, column 1 | 2 |
| Row 2, column 2 | 4 |
| Row 2, column 3 | 7 |
| Row 2, column 4 | 8 |
| Row 3, column 1 | 1 |
| Row 3, column 2 | 1 |
| Row 3, column 3 | 1 |
| Row 3, column 4 | 1 |
The page returns the 3×4 reduced row-echelon matrix, its rank, and pivot-column positions after scaled row reduction.
Assumptions and limits
- The input is a real 3×4 matrix and each cell is finite.
- Partial pivoting selects a large available pivot in the active column before normalization.
- A scale-aware tolerance treats sufficiently small floating-point values as zero.
- The output is reduced row-echelon form, which is stronger than merely clearing entries below pivots.
- The page does not infer whether the fourth column is an augmented right-hand side.
- Rank and pivot-column labels describe the supplied matrix, not a solution count for an unstated equation system.
- Exact rational arithmetic is not promised, so very ill-conditioned decimal matrices should be checked independently.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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