Introduction to Matrices definitions Flashcards
Introduction to Matrices definitions
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Matrix A rectangular arrangement of numbers in rows and columns used to organize and represent information, especially from systems of equations. Row A horizontal line of elements within a matrix, each corresponding to an equation in a system. Column A vertical line of elements within a matrix, each typically representing coefficients for a specific variable. Augmented Matrix A matrix that includes both the coefficients and constants from a system of equations, separated by a vertical bar. Coefficient A numerical factor in front of a variable within an equation, represented as an entry in a matrix. Constant A value in a system of equations not multiplied by a variable, appearing in the last column of an augmented matrix. Row Operation A manipulation applied to the rows of a matrix, including swapping, scaling, or adding rows, used to simplify matrices. Row Echelon Form A matrix form with ones along the diagonal and zeros below, enabling stepwise back substitution to solve equations. Reduced Row Echelon Form A matrix form with ones along the diagonal and zeros both above and below, directly revealing solutions without further substitution. Diagonal The set of entries in a matrix running from the top left to the bottom right, often targeted for ones in special forms. Back Substitution A process of solving for variables in a system by working upwards from the last equation after achieving row echelon form. Gaussian Elimination A method using row operations to transform a matrix into row echelon form, facilitating the solution of systems of equations. Gauss-Jordan Elimination A method using row operations to achieve reduced row echelon form, allowing immediate reading of solutions from the matrix. Zero Entry A matrix element with a value of zero, often created through row operations to simplify solving systems. Subscript Notation A labeling system for rows in matrices, using small numbers to indicate specific rows before and after operations.
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