# Help Needed for Vector Space Proof

## Main Question or Discussion Point

Hello

Well i hv just started vector spaces and well am finding difficulty in proving this hoffman and kunze problem could some 1 help me :(

Question : W1 and W2 be sub-spaces of vector space V such that set-theoritic union of W1 and W2 is also a Subspace . Proove that one of the subspace Wi is contained in other ?

Thank You

## Answers and Replies

Related Linear and Abstract Algebra News on Phys.org
so you have that W_1, W_2 are subspaces

you need to show that if W_1 U W_2 is a subspace then W_1 is contained in W_2, or W_2 is contained in W_1

the contrapositive is easier to prove, you should show that
if W_1 is not contained in W_2 and W_2 is not contained in W_1, then W_1 U W_2 is not a subspace
hint: W_1 U W_2 won't be closed under addition, show this and you are done

mathwonk
Science Advisor
Homework Helper
i.e. use contradiction.

Hey thanx was able to do the proof by proving the contradicton

Where is Applied maths

Please I wanna know if there is a forum that is talking about applied maths ..

If there. u can send me an e-mail at>>> ( ahmedtomyus@yahoo.com )

HallsofIvy
Science Advisor
Homework Helper
What do you mean by "applied maths"?