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, 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.
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