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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.