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Dimention of group question

  1. Jun 22, 2011 #1
    there is
    v1,..,vk,u,w vectors on space V
    the group {v1,..,vk,u} is independant
    [tex]Sp\{v1,..,vk\}\cap Sp\{u,w\}\neq\{0\}[/tex]
    find the dimention of sp{v1..vk,u,w}

    if {v1,..,vk,u} is independant then its span dimention is k+1
    and span so {v1,..,vk} independat to and dim sp{v1,..,vk}=k

    the dimention of sp{v1..vk,u,w} is
    dim(sp{v1..vk,u,w})=dim(sp{v1..vk}and sp{u,w}})=dim(sp{v1..vk}+sp{u,w})=dim(sp{v1..vk})+dim(sp{u,w})-dim(sp{v1..vk} intersect sp{u,w}})

    if v1..vk,u is independant then v1,..,vk is independant too so dim (sp{v1..vk})=k

    now regardingthe other two members i dont know
  2. jcsd
  3. Jun 23, 2011 #2
    You are given that u is indendent of v1,v2,...,vk.
    What does this imply about the intersection of the sapces spanned by {v1,v2...,vk} and {u}?
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