- #1

steelphantom

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## Homework Statement

If U1, U2, U3, are subspaces of a finite-dimensional vector space, then show

dim(U1 + U2 + U3) = dimU1 + dimU2 + dimU3 - dim(U1 [tex]\cap[/tex] U2) - dim(U1 [tex]\cap[/tex] U3) - dim(U2 [tex]\cap[/tex] U3) + dim(U1 [tex]\cap[/tex] U2 [tex]\cap[/tex] U3)

or give a counterexample.

## Homework Equations

## The Attempt at a Solution

I have the proof of the sum of the dimension of two subspaces in my book, so I would assume I would proceed in much the same way, but that "or give a counterexample" is making me just a little bit uneasy. I'm 90% sure that this is true, because basically the same formula holds for sets. Could anyone tell me if this is true before I proceed with my proof? It's going to be a long one if I use the same method the book did.