Proving Vector Space Subspace Union: Tips and Assistance"

[ambuj123]

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

 

[ircdan]

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]

i.e. use contradiction.

 

[ambuj123]

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

 

[tomyus]

Where is Applied maths

Please I want to 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]

What do you mean by "applied maths"?