A NOTE OF THE LINEAR BALANCE SYSTEMS FOR MATRIX X THAT SATISFIES
A linear system over the symmetrized max plus algebra has form with Ñ as a balance relation. The linear system is called the linear balance systems. This paper describes the necessary and sufficient condition of a solution of the linear balance systems with a matrix X that satisfies We obtain that if X is any matrix satisfying then has a solution if and only if in which case the most general solution is where h is arbitrary and
the symmetrized max plus algebra, matrix, inverse element, the linear balance systems.