{
  "unit": 8,
  "title": "Nonlinear Systems & Matrices",
  "terms": [
    {
      "en": "graphical solution",
      "es": "solución gráfica",
      "fr": "solution graphique",
      "ar": "حل بياني",
      "pt": "solução gráfica",
      "definition": "A point where graphs representing simultaneous equations intersect."
    },
    {
      "en": "solution set",
      "es": "conjunto solución",
      "fr": "ensemble des solutions",
      "ar": "مجموعة الحلول",
      "pt": "conjunto solução",
      "definition": "All ordered pairs or tuples satisfying each equation in a system."
    },
    {
      "en": "linear system",
      "es": "sistema lineal",
      "fr": "système linéaire",
      "ar": "نظام خطي",
      "pt": "sistema linear",
      "definition": "A set of equations in which each variable has degree at most one."
    },
    {
      "en": "substitution method",
      "es": "método de sustitución",
      "fr": "méthode de substitution",
      "ar": "طريقة التعويض",
      "pt": "método da substituição",
      "definition": "Solve one equation for a variable and replace it in another."
    },
    {
      "en": "nonlinear system",
      "es": "sistema no lineal",
      "fr": "système non linéaire",
      "ar": "نظام غير خطي",
      "pt": "sistema não linear",
      "definition": "A system containing at least one nonlinear equation."
    },
    {
      "en": "elimination method",
      "es": "método de eliminación",
      "fr": "méthode d'élimination",
      "ar": "طريقة الحذف",
      "pt": "método da eliminação",
      "definition": "Combine equations to cancel one variable."
    },
    {
      "en": "polynomial system",
      "es": "sistema polinómico",
      "fr": "système polynomial",
      "ar": "نظام كثيرات الحدود",
      "pt": "sistema polinomial",
      "definition": "A system of equations formed from polynomial expressions."
    },
    {
      "en": "rational system",
      "es": "sistema racional",
      "fr": "système rationnel",
      "ar": "نظام معادلات نسبية",
      "pt": "sistema racional",
      "definition": "A system containing rational expressions with excluded denominator values."
    },
    {
      "en": "radical system",
      "es": "sistema radical",
      "fr": "système à radicaux",
      "ar": "نظام معادلات جذرية",
      "pt": "sistema com radicais",
      "definition": "A system involving radicals and possible extraneous solutions."
    },
    {
      "en": "matrix",
      "es": "matriz",
      "fr": "matrice",
      "ar": "مصفوفة",
      "pt": "matriz",
      "definition": "A rectangular array of values arranged into rows and columns."
    },
    {
      "en": "matrix entry",
      "es": "elemento de matriz",
      "fr": "élément de matrice",
      "ar": "عنصر المصفوفة",
      "pt": "elemento de matriz",
      "definition": "A value at a specified row and column of a matrix."
    },
    {
      "en": "matrix dimensions",
      "es": "dimensiones de la matriz",
      "fr": "dimensions de matrice",
      "ar": "أبعاد المصفوفة",
      "pt": "dimensões da matriz",
      "definition": "The number of rows by the number of columns."
    },
    {
      "en": "augmented matrix",
      "es": "matriz ampliada",
      "fr": "matrice augmentée",
      "ar": "مصفوفة موسعة",
      "pt": "matriz aumentada",
      "definition": "A coefficient matrix with constants appended to encode a linear system."
    },
    {
      "en": "row reduction",
      "es": "reducción por filas",
      "fr": "réduction par lignes",
      "ar": "اختزال الصفوف",
      "pt": "redução por linhas",
      "definition": "Applying elementary row operations to simplify a matrix."
    },
    {
      "en": "determinant",
      "es": "determinante",
      "fr": "déterminant",
      "ar": "محدد المصفوفة",
      "pt": "determinante",
      "definition": "A scalar associated with a square matrix; nonzero implies invertibility."
    },
    {
      "en": "inverse matrix",
      "es": "matriz inversa",
      "fr": "matrice inverse",
      "ar": "المصفوفة المعكوسة",
      "pt": "matriz inversa",
      "definition": "A square matrix A^-1 satisfying AA^-1=I when it exists."
    },
    {
      "en": "linear transformation",
      "es": "transformación lineal",
      "fr": "transformation linéaire",
      "ar": "تحويل خطي",
      "pt": "transformação linear",
      "definition": "A map T preserving vector addition and scalar multiplication."
    }
  ],
  "schema_version": "1.1"
}