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.
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