Exercise 1.1.7

Question

Prove that $0\mathbf{v} = \mathbf{0}$ for any vector $\mathbf{v} \in V$.

Jing Huang · Accepted Answer

\begin{proof}
$0\mathbf{v} = (0\alpha)\mathbf{v} = \alpha(0\mathbf{v})$ for any scalar $\alpha$, so $(1-\alpha)0\mathbf{v}=0$ for all scalar $(1-\alpha)$. Then $0\mathbf{v} = \mathbf{0}$.
\end{proof}

Exercise 1.1.7

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Exercise 1.1.7

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