What Is the Dimension of Sp{v1,..,vk,u,w}?

[nhrock3]

there is
v1,..,vk,u,w vectors on space V
the group {v1,..,vk,u} is independent
and
Sp\{v1,..,vk\}\cap Sp\{u,w\}\neq\{0\}
find the dimension of sp{v1..vk,u,w}
?

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

the dimension 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 independent then v1,..,vk is independent too so dim (sp{v1..vk})=k

now regardingthe other two members i don't know

 

[talolard]

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}?