An Explicit Construction of Gauss-Jordan Elimination Matrix
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A constructive approach to get the reduced row echelon form of a given matrix A is presented. It has been shown that after the kth step of the Gauss-Jordan procedure, each entry a^k_ij(i<>j; j > k) in the new matrix A^k can always be expressed as a ratio of two determinants whose entries are from the original matrix A. The new method also gives a more general generalization of Cramer's rule than existing methods.
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