Gaussian Elimination Practice
Instructions
Row reduce the matrix one row operation at a time. Choose an operation below and click Apply (or press Enter). There are three kinds:
- Replace: add a multiple of one row to another, like R2 → R2 − 3R1 (enter −3 as the multiplier).
- Scale: multiply a row by a nonzero number, like R2 → (1/2)R2.
- Swap: exchange two rows, like R1 ↔ R3.
Multipliers can be integers, decimals, or fractions such as -3, 0.5,
or 1/2. Leading entries are circled, and the checklist shows which conditions
still fail. Every step is listed above the form; use Undo to take one back,
or Edit to change any step (the steps after it are redone).
Choose a Level to practice one skill at a time:
- Choose the row operations (the page computes the new rows).
- Compute the new rows (the page gives each row operation).
- Choose the row operations and compute the new rows.
- Do both, and also recognize when the matrix is in RREF.
Or, under Practice tasks, choose what to practice: choosing the row operations, computing the new rows, or both. If you don't choose the operations, the page gives each one, and you compute the new row. With Recognize when it's in RREF, the page doesn't tell you whether the matrix is in REF or RREF: say so yourself when you think it is (saying so too early counts as a hint). Rows you compute aren't checked automatically, so a mistake carries forward as it would on paper. To check your work, use Check (before applying a step) or Check all steps; each counts as a hint. Stuck? Hint suggests what to aim for next, and you can then ask for a more specific hint. Your work is saved in this page's address, so you can reload the page or share a link.