Elementary Operations and Gaussian Elimination

初等变换: Basic operations applied to rows or columns of a matrix.

高斯消元法: A method for solving systems of linear equations.

线性方程组: A collection of one or more linear equations involving the same variables.

系数矩阵: A matrix consisting of the coefficients of the variables in a system of linear equations.

未知矩阵: A matrix that contains the variables to be solved in a system of equations.

常数项: The term in an equation that does not contain any variables.

增广矩阵: A matrix that includes the coefficients and the constants from a system of linear equations.

初等行变换: Operations that can be performed on the rows of a matrix to manipulate it.

初等列变换: Operations that can be performed on the columns of a matrix.

行等价: Two matrices are row equivalent if one can be transformed into the other using elementary row operations.