Question: Given two vector spaces $V_{1}$ and $V_{2}$, prove that the dimension of their direct sum is $operatorname{dim}left(V_{1} oplus V_{2} ight)=operatorname{dim} V_{1}+operatorname{dim} V_{2}$.
Given two vector spaces $V_{1}$ and $V_{2}$, prove that the dimension of their direct sum is $\operatorname{dim}\left(V_{1} \oplus V_{2}\right)=\operatorname{dim} V_{1}+\operatorname{dim} V_{2}$.
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