Let u and v be distinct vectors in a vector space V. Show that {u,v} is linearly dependent if and only if u or v is a multiple of the other.
If $\displaystyle \{\bold{u},\bold{v}\}$ is inearly dependent it means $\displaystyle a\bold{u}+b\bold{v} = \bold{0}$ where $\displaystyle a,b$ are not both zero. WLOG say $\displaystyle a\not = 0$ then $\displaystyle \bold{u} = -\frac{b}{a}\bold{v}$. And that is a multiple of the other.