Linear Algebra: Operations with Vector Spaces

[looper]

Homework Statement

Let V be a vector space over k and S the set of all subspaces of V. Consider the operation of subspace addition in S. Show that there is a zero in S for this operation and that the operation is associative. Consider the operation of intersection in S. Show that this operation is associative. Is there an identity for this operation (i.e., there is an E existing in S such that A intersect E = A for all E in S)?

Homework Equations

The Attempt at a Solution

Let U and W be in S. Then U+W=W+U=0+0. U intersect W = W intersect U...I'm not really sure where else to go with this...

 

[HallsofIvy]

What do you mean by "subspace addition"? The direct product? You say "U+ W= W+ U= 0+ 0". What is "0"?

 

[cookiesyum]

What do you mean by "subspace addition"? The direct product? You say "U+ W= W+ U= 0+ 0". What is "0"?

I guess the 0 that E U and the 0 that E W? You know, I'm not really sure. We're not using a published book for my Linear Algebra class. We have pdf pages of the professor's lecture notes but they are really short (very minimal explanations), full of typos, and examples without solutions. To be honest, I'm not really sure even what the question is asking. =/