## 403/503 – HW1

Use the axioms of vector space to verify that if $V$ is a vector space over a field $\mathbb F$, then:

1. For any $v\in V$, we have $(-1)v=-v$,
2. For any $v\in V$, we have $0v=\vec 0$, and
3. For any $r\in\mathbb F$, we have $r\vec 0=\vec 0$.

(Due January 20, at the beginning of lecture.)