Question

Consider the system of equations A ⊗ x = b where
(i) A ∈ R
m×n
max , x ∈ R
n
max, b ∈ R
m
max and Rmax = R ∪ {−∞},
(ii) ⊗ denotes the max-plus matrix (or matrix-vector) product based
on the arithmetic operations of ”addition” a ⊕ b := max(a, b) and
”multiplication” a ⊗ b := a + b.
Formulate and prove:
(i) Necessary and sufficient conditions for existence of a solution,
(ii) Necessary and sufficient conditions for uniqueness of a solution