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Determinants and Cramer's Rule definitions

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  • Determinant
    A single value calculated from a square matrix using a specific formula, often used to solve systems of equations.
  • 2x2 Matrix
    A grid with two rows and two columns, often used as the simplest case for determinant calculations.
  • 3x3 Matrix
    A square array with three rows and three columns, requiring a more complex process to find its determinant.
  • Diagonal
    A set of elements in a matrix running from one corner to the opposite, crucial for determinant calculations.
  • Cramer's Rule
    A formulaic method using determinants to directly solve systems of linear equations for each variable.
  • Coefficient Matrix
    A matrix composed of the coefficients of variables from a system of equations, used in determinant calculations.
  • Augmented Matrix
    A matrix that includes both the coefficients and constants from a system of equations, aiding in systematic solutions.
  • Constant Column
    The column in an augmented matrix containing the constants from the right side of each equation.
  • Submatrix
    A smaller matrix formed by removing specific rows and columns from a larger matrix, used in determinant expansion.
  • Minor
    The determinant of a submatrix, found by deleting a row and column from the original matrix.
  • Alternating Signs
    A pattern in determinant expansion where the signs of terms switch between positive and negative.
  • Solution Vector
    A set of values for the variables in a system of equations, found using Cramer's rule.
  • Quotient of Determinants
    The result of dividing one determinant by another, yielding the value of a variable in Cramer's rule.
  • Coefficient
    A numerical factor multiplying a variable in an equation, forming the entries of the coefficient matrix.
  • System of Equations
    A collection of two or more equations with shared variables, often solved using matrices and determinants.