Row Reduction Workbench

1. Enter a matrix

Each challenge checks itself. Work on this keeps it in view above the controls.

Type a matrix (up to 4x6), apply row operations with exact fraction arithmetic, undo, and get told when you reach REF and RREF; a step that undoes progress gets a warning, and a missed elimination a tip with the right multiplier.

How to use

1. Load an example, or choose the size, type the entries and press Use this matrix. For a system, keep the augmentation bar before the last column. For [A | I], put the bar in the middle.
2. Choose an operation, the rows, and the multiplier c, check the preview line, then press Apply (or press Enter in the multiplier box).
3. All arithmetic is exact: fractions stay fractions (for example 5/2), never rounded decimals.
4. The workbench tells you when the matrix reaches row echelon form (REF) and reduced row echelon form (RREF), marks the pivots (bold with a box), and lists pivot columns and free variables. For a system in RREF it writes the solution in parametric vector form.
5. Undo steps back one operation; Start over returns to the matrix you entered.
6. Suggest the next step fills in the operation form with the next Gauss–Jordan step (clear each pivot column completely, above and below, before moving right). You still press Apply.
7. Keyboard: every control is a standard form field. Screen readers announce each step and the new form of the matrix; the matrix is a table with row and column headers.

Notation

Written in the standard notation: R_i ← R_i + cR_j, R_i ↔ R_j, R_i ← cR_i.

Accessibility: every control is a standard form control you can reach with Tab and change with the arrow keys; the status box is announced by screen readers; the picture has a text description (press Describe) that updates as you work; animations are skipped when your system asks for reduced motion.