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Let $U \subset V$ and $W$ be finite dimensional linear spaces and $L: V \rightarrow W$ a linear map. Show that
$\operatorname{dim}\left(\left.\operatorname{ker} L\right|_{U}\right) \leq \operatorname{dim} \operatorname{ker} L=\operatorname{dim} V-\operatorname{dim} \operatorname{Im}(L)$
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