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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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