This sandbox was generated by Claude (Anthropic) for the Linear Algebra 101 course materials, and is built for Module 3 (Systems of Linear Equations). Type the coefficients of a system A x = b — 2×2 or 3×3 — and watch Gaussian elimination with partial pivoting run one row operation at a time to row echelon form, the determinant appear as the product of the pivots, and the system be classified as having a unique solution, no solution, or infinitely many. For a 2×2 system each equation is drawn as a line: crossing lines are the unique solution, parallel distinct lines are no solution, one line drawn twice is infinitely many. Every step, every pivot and the drawn crossing are computed from your coefficients — never sketched.

The determinant decides a square system. When det(A) ≠ 0 the rows are independent and there is exactly one solution for every b; the page confirms it two independent ways — back-substitution on the echelon form and Cramer's rule — and shows the two agree. When det(A) = 0 the page compares rank(A) with rank([A | b]) to tell no solution from infinitely many; both ranks are counted from the echelon form the elimination produced.

Notation follows the course: column vectors, m × n = rows × columns, the augmented matrix [A | b], a pivot as the leading nonzero entry of a row, and the row operation Rᵢ → Rᵢ − (aᵢₖ/aₖₖ) Rₖ.

What is chosen rather than computed: the default system, the preset systems (each labelled where it is selected), and the extent of the drawn grid. Nothing here is a measurement; it is arithmetic, done rather than imitated.