Exercise 1.1.8

Question

Prove that for any vector $\mathbf{v}$ its additive inverse $-\mathbf{v}$ is given by $(-1)\mathbf{v}$.

Jing Huang · Accepted Answer

\begin{proof}
$\mathbf{v} + (-1)\mathbf{v} = (1-1)\mathbf{v} = 0\mathbf{v} = \mathbf{0}$ and we know form \href{./exercise_1-6}{Problem 1.6} that the additive inverse is unique. So $-\mathbf{v} = (-1)\mathbf{v}$.
\end{proof}

Exercise 1.1.8

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Exercise 1.1.8

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