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Math Help - Linear Dependance/Independance

  1. #1
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    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.
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    Quote Originally Posted by leungsta View Post
    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.
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  3. #3
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    perfect!! Thanks alot! Your help is much appreciated..
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