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Determinants and Cramer's Rule definitions Flashcards

Determinants and Cramer's Rule definitions
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  • Determinant
    A single value calculated from a square matrix using a specific formula, crucial for solving systems and understanding matrix properties.
  • 2x2 Matrix
    A grid with two rows and two columns, often used as the simplest case for determinant calculation and Cramer's rule.
  • 3x3 Matrix
    A square array with three rows and three columns, requiring reduction to smaller matrices for determinant evaluation.
  • Diagonal
    A set of elements running from one corner of a matrix to the opposite, used in determinant calculations for multiplying and subtracting products.
  • Cramer's Rule
    A formulaic method for solving systems of linear equations by dividing determinants of matrices with replaced columns.
  • Augmented Matrix
    A matrix that includes both the coefficients and constants from a system of equations, organized for systematic solution methods.
  • Coefficient
    A numerical factor in front of a variable within an equation, forming the entries of matrices used in Cramer's rule.
  • Constant
    A value on the right side of an equation, substituted into matrix columns when applying Cramer's rule.
  • Minor
    A smaller matrix formed by removing a row and column from a larger matrix, used in calculating higher-order determinants.
  • Sign Alternation
    A pattern of switching plus and minus signs when expanding determinants, especially in 3x3 matrices.
  • System of Equations
    A set of two or more equations with multiple variables, often solved using matrices and determinants.
  • Quotient
    The result of dividing one determinant by another in Cramer's rule to find variable values.
  • Matrix Notation
    A symbolic way to represent matrices, often using brackets or vertical bars, indicating determinants or matrix structure.
  • Replacement Column
    A column in a matrix substituted with constants when applying Cramer's rule to solve for a specific variable.
  • Zero Element
    An entry in a matrix with a value of zero, which can simplify determinant calculations by eliminating terms.