Let u and v be distinct vectors in a vector space V show that {u,v} is linearly dependant if and only if u or v is a multiple of the other.

Thanks in advance.

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- Jan 19th 2010, 06:25 PMMatharchLinear dependence
Let u and v be distinct vectors in a vector space V show that {u,v} is linearly dependant if and only if u or v is a multiple of the other.

Thanks in advance. - Jan 19th 2010, 06:56 PMJameson
A set of vectors are linearly dependent if vectors $\displaystyle v_1 , v_2, ... v_n$ satisfy $\displaystyle a_1 v_1 + a_2 v_2 + ...a_n v_n=0$ where a_i is a scalar and the set of scalars are not all 0.

So applying this to your problem, you have two vectors. Assume that they are linearly dependent then apply the definition and you can easily show u or v is a multiple of the other. Then assume one is a multiple of the other and show that when this is true the two vectors satisfy the definition of lin. dep. - Jan 20th 2010, 05:51 AMMatharch
Thank you very much that's what I thought but I wasn't sure.