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?
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.