Another linear algebra question! What a surprise!(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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 gonna be a long one if I use the same method the book did.

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# Homework Help: Lin. Algebra - Sum of Dim. of Three Subspaces

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