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.

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- Sep 13th 2008, 04:51 PMleungstaLinear 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.

- Sep 13th 2008, 04:57 PMThePerfectHacker
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.

- Sep 13th 2008, 05:30 PMleungsta
perfect!! Thanks alot! Your help is much appreciated..