there is U,W,V subspaces of and dimU=dimV=dimW=3

prove that

how i tried to solve it:

dim(U+V)=dimU+dimV-

because U+V is a subspace of then

so

because is a subspace of then

by inputing the previos data i get

is it correct?

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- June 24th 2011, 03:55 PMtransgalacticR^4 subspace question
there is U,W,V subspaces of and dimU=dimV=dimW=3

prove that

__how i tried to solve it:__

dim(U+V)=dimU+dimV-

because U+V is a subspace of then

so

because is a subspace of then

by inputing the previos data i get

is it correct? - June 24th 2011, 08:26 PMFernandoRevillaRe: R^4 subspace question
- June 24th 2011, 10:21 PMDevenoRe: R^4 subspace question
indeed, we have 4 = dim(R^4) ≥ dim(U+V) = dim(U) + dim(V) - dim(U∩V) = 6 - dim(U∩V).

this means that dim(U∩V) ≥ 6-4 = 2.

now we also have 4 ≥ dim((U∩V)+W) = dim(U∩V) + dim(W) - dim((U∩V)∩W) ≥ 5 - dim(U∩V∩W).

this means that dim(U∩V∩W) ≥ 5-4 = 1. - June 24th 2011, 11:57 PMtransgalacticRe: R^4 subspace question
ok i understand now

thanks