Question
For $F, G \in \operatorname{Hom}(V, U),$ show that $\operatorname{rank}(F+G) \leq \operatorname{rank}(F)+\operatorname{rank}(G) .$ (Here $V$ has finite dimension.)
Step 1
Recall the definition of rank: The rank of a linear transformation $F: V \to U$ is the dimension of its image, i.e., $\operatorname{rank}(F) = \dim(\operatorname{Im}(F))$. Show more…
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