Questionfield $\mathbb{R}$. Find the following: the sum: 6 田 $-5=$ $\square$ the scalar multiple: 7 ■ $6=$ $\square$ the zero vector: $\underline{0}_{V}=$ $\square$ the additive inverse of $x$ : 日 $x=$ $\square$
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Studdy Solution
Find the additive inverse $\boxminus x$ such that $x \boxplus (\boxminus x) = \underline{0}_{V}$.
Using the vector addition definition:
$$x \boxplus (\boxminus x) = x + (\boxminus x) + 2 = -2$$
Solving for $\boxminus x$:
$$x + (\boxminus x) + 2 = -2$$ $$\boxminus x = -2 - 2 - x$$ $$\boxminus x = -x - 4$$
The additive inverse is:
$$\boxed{-x - 4}$$