Computer Science – Symbolic Computation
Scientific paper
2009-07-29
Computer Science
Symbolic Computation
Scientific paper
A constructive approach to get the reduced row echelon form of a given matrix $A$ is presented. It has been shown that after the $k$th 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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