Bridging Gauss-Jordan Reduction and Determinant Methods Through 
Cross-Multiplication-Flip (CMF) Method in Matrix Inversion 
and Solving Systems of Linear Equations

Judel Villas Protacio

doi:10.20944/preprints202307.0070.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 3 July 2023 / Approved: 3 July 2023 / Online: 4 July 2023 (03:11:01 CEST)

In this paper, we introduce as a pedagogical strategy an internal division-free, straightforward, and symmetrically progressing algorithm in manually computing matrix inverse and solving systems of linear equations by revisiting the application of elementary row operations in the Gauss-Jordan reduction method and connecting it to the determinant method. The proposed cross-multiplication-flip (CMF) algorithm employs cross-multiplication similar to the butterfly movement in computing determinants as a strategic application of elementary row operations to efficiently reduce the rows and then applies flipping of rows and entries to put an upper triangular matrix into lower triangular form to continue the reduction process.

matrix inverse; systems of linear equations; cross-multiplication; Gauss-Jordan reduction; determinant method

Computer Science and Mathematics, Computational Mathematics

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Bridging Gauss-Jordan Reduction and Determinant Methods Through Cross-Multiplication-Flip (CMF) Method in Matrix Inversion and Solving Systems of Linear Equations

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