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Gregoria Ariyanti
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Journal : JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI

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Necessary and Sufficient Conditions for The Solutions of Linear Equation System Gregoria Ariyanti
Jurnal Matematika, Statistika dan Komputasi Vol. 17 No. 1 (2020): JMSK, SEPTEMBER, 2020
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/jmsk.v17i1.10352

Abstract

A Semiring is an algebraic structure (S,+,x) such that (S,+) is a commutative Semigroup with identity element 0, (S,x) is a Semigroup with identity element 1, distributive property of multiplication over addition, and multiplication by 0 as an absorbent element in S. A linear equations system over a Semiring S is a pair (A,b)  where A is a matrix with entries in S  and b is a vector over S. This paper will be described as necessary or sufficient conditions of the solution of linear equations system over Semiring S viewed by matrix X  that satisfies AXA=A, with A in S.  For a matrix X that satisfies AXA=A, a linear equations system Ax=b has solution x=Xb+(I-XA)h with arbitrary h in S if and only if AXb=b.
Co-Authors Ana Easti Rahayu Maya Sari Angga Rahabistara Sumadji Ari Suparwanto ARI SUPARWANTO Ari Suparwanto Budi Surodjo David Ary Wicaksono Devy Yuliastri Kurnia Putri Devy Yuliastri Kurnia Putri, Devy Elisabeth Ungaria Ega Puspitasari Epi Jiem Pania Fransiskus Gatot Santoso Hendry Vebriana, Yemima Intan Nurditasari Kristin Anggraini Laurensia Youlanda Alviandita Maria Josephine Kriesye Mariani Dian Marlince Pati Bebe Martaningrum, Melita Mateus Yumarnamto Melita Martaningrum Natalis Nero Patalas Novia Sukma Dia Pertiwi Nurditasari, Intan Pania, Epi Jiem Patalas, Natalis Nero Pati Bebe, Marlince Puspitasari, Elisabeth Ungaria Ega Resty Rahajeng Santoso, Fransiskus Gatot Iman Sari, Wiyola Nensiana Septia Dana, Theressa Sukma Dia Pertiwi, Novia Theressa Septia Dana Ungaria Ega Puspitasari, Elisabeth Vebriana, Yemima Hendry Wiyola Nensiana Sari Yashinta, Acintya Pramudita Yemima Hendry Vebriana Youlanda Alviandita, Laurensia Yustinus Setio Laksono Yustinus Setio Laksono, Yustinus Setio