Possible Duplicate:
The calculation of $\dim(U + V + W)$
Given a linear space $V$ and subspaces $A_i \subseteq V$ such that $1\leq i \leq n.$
To find $\dim(A_1 + A_2 +\cdots + A_n)$ it seems we can use inclusion exclusion. Is there any other way of finding it?