- Thread starter
- Moderator
- #1

- Jan 26, 2012

- 995

-----

**Problem**: Suppose we are given an exact sequence of finite dimensional $K$-vector spaces and $K$-linear maps:

\[0\rightarrow V_1\rightarrow V_2\rightarrow\cdots\rightarrow V_n\rightarrow 0.\]

Prove that

\[\sum\limits_{i=1}^n (-1)^i\dim(V_i) = 0.\]

-----

**Hint**:

Remember to read the POTW submission guidelines to find out how to submit your answers!