Answer
(0,0,2,2) , (2,3,1,1)
Work Step by Step
calculations in$ \; \mathbb{Z}_{n}$ are made modulo n:
$2\;\;[\;(3,1,1,2)\;+\;\;(3,3,2,1)\;]\;\;=\;\;2[(6,4,3,3)]\;\;=(12,8,6,6)\\\\$
In $\mathbb{Z}_{4}^{4}$ apply to:
$(12,8,6,6){\color{Cyan}\Rightarrow }\;\;\;(0,0,2,2)\\\\$
In $\mathbb{Z}_{5}^{4} $apply to:
$(12,8,6,6){\color{Cyan}\Rightarrow }\;\;\;(2,3,1,1)$
