PreprintArticleVersion 1Preserved in Portico This version is not peer-reviewed
Bridging Gauss-Jordan Reduction and Determinant Methods Through
Cross-Multiplication-Flip (CMF) Method in Matrix Inversion
and Solving Systems of Linear Equations
Version 1
: Received: 3 July 2023 / Approved: 3 July 2023 / Online: 4 July 2023 (03:11:01 CEST)
How to cite:
Protacio, J. V. Bridging Gauss-Jordan Reduction and Determinant Methods Through
Cross-Multiplication-Flip (CMF) Method in Matrix Inversion
and Solving Systems of Linear Equations. Preprints2023, 2023070070. https://doi.org/10.20944/preprints202307.0070.v1
Protacio, J. V. Bridging Gauss-Jordan Reduction and Determinant Methods Through
Cross-Multiplication-Flip (CMF) Method in Matrix Inversion
and Solving Systems of Linear Equations. Preprints 2023, 2023070070. https://doi.org/10.20944/preprints202307.0070.v1
Protacio, J. V. Bridging Gauss-Jordan Reduction and Determinant Methods Through
Cross-Multiplication-Flip (CMF) Method in Matrix Inversion
and Solving Systems of Linear Equations. Preprints2023, 2023070070. https://doi.org/10.20944/preprints202307.0070.v1
APA Style
Protacio, J. V. (2023). Bridging Gauss-Jordan Reduction and Determinant Methods Through
Cross-Multiplication-Flip (CMF) Method in Matrix Inversion
and Solving Systems of Linear Equations. Preprints. https://doi.org/10.20944/preprints202307.0070.v1
Chicago/Turabian Style
Protacio, J. V. 2023 "Bridging Gauss-Jordan Reduction and Determinant Methods Through
Cross-Multiplication-Flip (CMF) Method in Matrix Inversion
and Solving Systems of Linear Equations" Preprints. https://doi.org/10.20944/preprints202307.0070.v1
Abstract
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.
Keywords
matrix inverse; systems of linear equations; cross-multiplication; Gauss-Jordan reduction; determinant method
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.