Necessary and Sufficient Conditions for The Solutions of Linear Equation System


  • Gregoria Ariyanti Prodi Pendidikan Matematika Universitas Katolik Widya Mandala Surabaya



semiring, linear equations system, matrix


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.


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How to Cite

Ariyanti, G. (2020). Necessary and Sufficient Conditions for The Solutions of Linear Equation System. Jurnal Matematika, Statistika Dan Komputasi, 17(1), 82-88.



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