(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let U, W be subspaces of a vector space V. Show that dim(U+W) = dim(U) + dim (W) - dim (U intersect W).

2. Relevant equations

3. The attempt at a solution

I can see this picture-wise in a venn-diagram form. In adding U and W you count the elements in their intersection twice, since both spaces contain them. Thus, you subtract the dimension of U intersect W. But, how do you show this in proof format? It doesn't seem like a verbal explanation is enough.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Dimension Proof?

**Physics Forums | Science Articles, Homework Help, Discussion**