{
  "schemaVersion": 1,
  "publisher": "Eucalyptus One LLC",
  "product": "math-workbench",
  "tool": "rref",
  "title": "Gaussian elimination / RREF",
  "scope": "Free website calculator example; not a report from the pre-release application.",
  "calculatorUrl": "https://eucalyptusone.com/tools/math/rref/",
  "inputs": {
    "A": "1 2 5\n3 4 11"
  },
  "inputLabels": {
    "A": "Matrix A"
  },
  "result": {
    "title": "Gaussian elimination / RREF",
    "subtitle": "Exact row-operation trace",
    "summary": "RREF(A) =\n[ 1  0  1 ]\n[ 0  1  2 ]\nRank = 2",
    "steps": [
      {
        "title": "Original matrix",
        "body": "[ 1  2   5 ]\n[ 3  4  11 ]"
      },
      {
        "title": "Eliminate column 1 in row 2",
        "body": "R2 <- R2 - (3) * R1\n[ 1   2   5 ]\n[ 0  -2  -4 ]"
      },
      {
        "title": "Normalize pivot in row 2",
        "body": "R2 <- R2 / (-2)\n[ 1  2  5 ]\n[ 0  1  2 ]"
      },
      {
        "title": "Eliminate column 2 in row 1",
        "body": "R1 <- R1 - (2) * R2\n[ 1  0  1 ]\n[ 0  1  2 ]"
      }
    ],
    "table": null,
    "chart": null,
    "warnings": [],
    "verification": "Pivot columns (1-indexed): 1, 2"
  },
  "assumptions": "Supports 1–7 rows and 1–7 columns with exact integers, finite decimals, or fractions. Scientific notation exponents are limited to ±15. Rational numerators and denominators are capped below 260 digits. Rank refers to the entire supplied matrix, including any augmented column.",
  "provenance": "Selected exact rational and row-reduction functions from Math Workbench beta 0.5."
}