Dimension of the Union of two subspaces

[Estela]

Hello!

If I'm asked to determine the dimension of the union of two subspaces (E) U (F), and I know that E has dimension 5 and F has dimension 3, and that F belongs to E. So what is the dimension of the subspace generated by E U F? is it 3 or 5?

Thank you very much for your help!

Estela

 

[Ishuda]

Hello!

If I'm asked to determine the dimension of the union of two subspaces (E) U (F), and I know that E has dimension 5 and F has dimension 3, and that F belongs to E. So what is the dimension of the subspace generated by E U F? is it 3 or 5?

Thank you very much for your help!

Estela

When you say 'F belongs to E' do you mean F is a subset of E [or possibly more appropriately F is isomorphic to a subset of E]? If so, then the union of F and E is just E [a set isomorphic to E]. That is, a union of two sets is what is in both sets and since F is a subset of E, what is in both sets is E.