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If n= m, then it is obvious from the construction of the algorithm that the matrix A will turn out to be singular, which is what we needed. First, the second row is divided by A, then subtracted from all other rows with coefficients such as resetting the second column of the matrix A.Īnd so on until we process all rows or columns of matrix A. Similarly, the second step of the algorithm is performed only now the second column and the second row are considered. Then the algorithm adds the first row to the rest of the rows with such coefficients that their coefficients in the first column turn to zeros - for this, when adding the first row to the i-th, it is necessary to multiply it by -A.įor each operation with matrix A (division by a number and addition to one row by another), the corresponding operations are performed with vector b in a sense, it behaves as if it were the m+1st column of matrix A.Īs a result, at the end of the first step, the first column of matrix A will become single (i.e., it will contain one in the first row and zeros in the rest). The Gauss-Jordan algorithm divides the first row by coefficient A at the first step. This is a method of sequential exclusion of variables when using elementary transformations, the system of equations is reduced to an equivalent system of triangular form.Īll the system variables are sequentially located, starting from the last (by number). The Gauss method is a classical method for solving linear algebraic equations (SLA) systems. FUNCIONES DE FECHA Y HORA ｜ SQL SERVER Using the Gaussian Elimination Method in Matlab