take all vectors of the form {3k, 3k} k in I. This forms a vector subspace of I. So do vectors of the form say {5k, 5k}. But clearly their union is not a subspace as {8k,8k} is not in the space for all k so it's not closed under addition.
So I have Vector space V over the field F. And we have two subspaces U,W (subspaces of V)
There is a claim here saying that the intersection of the subspaces U and W is a vector space too, but their unity is not a subspace.
How come their unity is not a subspace? Shouldn't their unity be equal to the subspace U+W since that it's going to be closed under addition and multiplication with scalars? What am I missing here?
take all vectors of the form {3k, 3k} k in I. This forms a vector subspace of I. So do vectors of the form say {5k, 5k}. But clearly their union is not a subspace as {8k,8k} is not in the space for all k so it's not closed under addition.