## Linear Algebra: A Modern Introduction

$$[1,1,0]$$
First, compute the sum in $\mathbb{Z^3}$: $$[2,1,2]+[2,0,1]=[4,1,3]$$ To convert this to $\mathbb{Z^3_3}$, find the remainder of each component when divided by $3$, yielding the solution of $$[1,1,0]$$