How to use
Enter a rectangular matrix of up to 4 rows and 4 columns. Use integers, fractions such as 1/3, or decimal points. Calculate to see the exact RREF, pivot columns and row operations. The matrix above the fields follows your draft; the Result is confirmed only by Calculate.
Read the result
Rank counts nonzero rows in RREF and the number of independent columns. Pivots are numbered from 1 in the original column order. Swapping rows, scaling by a nonzero value and adding a multiple of another row preserve row equivalence. Only changed rows are highlighted at each step. E records those operations and E·A = RREF is checked exactly.
Example
1 2 3; 0 2 4 becomes 1 0 -1; 0 1 2. Rank is 2 and pivot columns are 1, 2. For a fractional example, 1/2 1/3; 1 2/3 reduces to 1 2/3; 0 0, with rank 1. A zero matrix has rank 0.
Limits and errors
Maximum 4×4, 500 input characters, 24 characters per number, 6 decimal places; input numerator and denominator magnitudes at most 10⁹. Intermediate reduced numerators and denominators have a 256-bit cap. No symbols or scientific notation. A zero denominator is invalid. Fractions remain exact rather than rounding to two decimals.
Frequently asked questions
Does a final column represent a right-hand side?
Every column is treated as part of the matrix, including any augmented column you enter. Rank refers to that entire matrix. This tool does not label unique, infinite or inconsistent solutions; use the pivot structure with your own system definition.
Can I edit or copy the result?
Editing invalidates the confirmed result and disables Copy. Calculate again before copying. Clear leaves the fields empty. The pale example runs immediately; the first focus in a value field clears all example values once.
Sources: TU Delft · Linear algebra