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Math Help - lenear dependance proof

  1. #1
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    lenear dependance proof

    suppose that v1..vk is an independant group
    and (v1+w),(v2+w)... (vk+w) is dependant group
    prove that w is a lenear combination of v1,v2,..vn

    how i tried to solve:
    a1v1+...akvk=0
    if a1=0 a2=0 .. ak=0 (trivial solution)

    and
    b1(v1+w) +b2(v2+w) +..bk(vk+w)=0

    b coefficients cannot be all zeros

    b1v1+b2v2+..bkvk +w(b1+..bk)=0

    what now
    ?
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  2. #2
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    The sum b1 + ... + bk cannot be 0; otherwise, v1, ..., vk would be dependent. Move w(b1+..bk) to the right-hand side and divide both sides by b1+ ... + bk.
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