![]() ![]() ![]() The second stage is not so essential for solving linear systems of equations because the Gauss-Jordan method is inefficient for practical calculations. When a linear system of equations is solved numerically, it nearly always uses Gaussian elimination. This algorithm utilizes row operations to put the augmented matrix into a special form, which is usually called as Gauss-Jordan elimination it consists of two stages, a forward phase (usually referred to as Gaussian elimination) in which matrix is transferred to a kind of upper triangular or "steplike" matrix (see the previous section), and a backward phase in which zeroes are introduced in each column containing a pivot using row operations. This form is known as the reduced row echelon form, which is usually abbreviated as rref. ![]() In this section, we discuss the algorithm for reducing any matrix, whether or not the matrix is viewed as an augmented matrix for linear system, to a simple form that could be used for further analysis and/or computation. Reduce Row Reduction Form (RREF) Carl Gauss Computer solves Systems of Linear Equations. ![]()
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