Chapter 1 - Vectors - 1.1 The Geometry and Algebra of Vectors - Exercises 1.1 - Page 17: 42

$$[1,1,2]$$

Work Step by Step

First, compute the product in $\mathbb{Z}^3$: $$2[2,2,1]=[4,4,2]$$ Now, divide each term by $3$ and find the remainder, to convert the above to $\mathbb{Z}^3_3$: $$[1,1,2]$$

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