# Math Help - Linear Dependance/Independance

1. ## Linear Dependance/Independance

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.

2. Originally Posted by leungsta
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 $\{\bold{u},\bold{v}\}$ is inearly dependent it means $a\bold{u}+b\bold{v} = \bold{0}$ where $a,b$ are not both zero. WLOG say $a\not = 0$ then $\bold{u} = -\frac{b}{a}\bold{v}$. And that is a multiple of the other.

3. perfect!! Thanks alot! Your help is much appreciated..