CRAMER’S RULE IN MIN-PLUS ALGEBRA
Cramer’s rule is one of a method for solving a system of linear equations in conventional algebra. The system of linear equation can be solved using Cramer’s rule if . Max-plus algebra is a set where is a set of real numbers, equipped with biner operations and where and . Min-plus Alge...
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Universitas Pattimura
2024-05-01
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| Online Access: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/12015 |
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| author | Zakia Nur Ramadhani Putri Siswanto Siswanto Vika Yugi Kurniawan |
| author_facet | Zakia Nur Ramadhani Putri Siswanto Siswanto Vika Yugi Kurniawan |
| author_sort | Zakia Nur Ramadhani Putri |
| collection | DOAJ |
| description | Cramer’s rule is one of a method for solving a system of linear equations in conventional algebra. The system of linear equation can be solved using Cramer’s rule if . Max-plus algebra is a set where is a set of real numbers, equipped with biner operations and where and . Min-plus Algebra is a set where is a set of real numbers, equipped with biner operations and where and . In max-plus algebra has been formulated Cramer’s rule to solve a system of linear equations. Because max-plus algebra is isomorphic to min-plus algebra, Cramer’s rule can be formulated into min-plus algebra. The purpose of this research is to determine the sufficient conditions for a system of linear equations can be solved using Cramer’s rule. The method used in this research is a literature study that reviews previous research related to min-plus algebra, max-plus algebra, and Cramer’s rule in max-plus algebra. By using the appropriate analogy in max-plus algebra, we can determine the sufficient conditions so that a system of linear equations in min-plus algebra can be solved using Cramer’s rule. Based on the research, the sufficient conditions for a system of linear equations can be solved using Cramer’s rule are for and with the Cramer’s rule is . For an invertible matrix A, Cramer’s rule can be written as . |
| format | Article |
| id | doaj-art-376cee4c5bc046e1ba0a524edba29c42 |
| institution | Kabale University |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Universitas Pattimura |
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| series | Barekeng |
| spelling | doaj-art-376cee4c5bc046e1ba0a524edba29c422025-08-20T03:35:54ZengUniversitas PattimuraBarekeng1978-72272615-30172024-05-011821147115410.30598/barekengvol18iss2pp1147-115412015CRAMER’S RULE IN MIN-PLUS ALGEBRAZakia Nur Ramadhani Putri0Siswanto Siswanto1Vika Yugi Kurniawan2Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Sebelas Maret, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, University of Sebelas Maret, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, University of Sebelas Maret, IndonesiaCramer’s rule is one of a method for solving a system of linear equations in conventional algebra. The system of linear equation can be solved using Cramer’s rule if . Max-plus algebra is a set where is a set of real numbers, equipped with biner operations and where and . Min-plus Algebra is a set where is a set of real numbers, equipped with biner operations and where and . In max-plus algebra has been formulated Cramer’s rule to solve a system of linear equations. Because max-plus algebra is isomorphic to min-plus algebra, Cramer’s rule can be formulated into min-plus algebra. The purpose of this research is to determine the sufficient conditions for a system of linear equations can be solved using Cramer’s rule. The method used in this research is a literature study that reviews previous research related to min-plus algebra, max-plus algebra, and Cramer’s rule in max-plus algebra. By using the appropriate analogy in max-plus algebra, we can determine the sufficient conditions so that a system of linear equations in min-plus algebra can be solved using Cramer’s rule. Based on the research, the sufficient conditions for a system of linear equations can be solved using Cramer’s rule are for and with the Cramer’s rule is . For an invertible matrix A, Cramer’s rule can be written as .https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/12015cramer's rulemin-plus algebrasystem of linear equation |
| spellingShingle | Zakia Nur Ramadhani Putri Siswanto Siswanto Vika Yugi Kurniawan CRAMER’S RULE IN MIN-PLUS ALGEBRA Barekeng cramer's rule min-plus algebra system of linear equation |
| title | CRAMER’S RULE IN MIN-PLUS ALGEBRA |
| title_full | CRAMER’S RULE IN MIN-PLUS ALGEBRA |
| title_fullStr | CRAMER’S RULE IN MIN-PLUS ALGEBRA |
| title_full_unstemmed | CRAMER’S RULE IN MIN-PLUS ALGEBRA |
| title_short | CRAMER’S RULE IN MIN-PLUS ALGEBRA |
| title_sort | cramer s rule in min plus algebra |
| topic | cramer's rule min-plus algebra system of linear equation |
| url | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/12015 |
| work_keys_str_mv | AT zakianurramadhaniputri cramersruleinminplusalgebra AT siswantosiswanto cramersruleinminplusalgebra AT vikayugikurniawan cramersruleinminplusalgebra |