\begin{align*}
0 \to U \xrightarrow{f} V \xrightarrow{g} W \to 0
\end{align*}
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be a short exact sequence of vector spaces over $k$. If at least two of the vector spaces $U$, $V$, and $W$ are finite-dimensional over $k$, then the remaining vector space is finite-dimensional over $k$, and
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\begin{align*}
\dim_k V = \dim_k U + \dim_k W.
\end{align*}