Does an injective $\mathbb F_9$ vector space homomorphism $\mathbb F_9^5 \to \mathbb F_9^3$ exist?
Is it able to solve that task by some technique? If so, how is it working then?
2026-04-01 22:21:26.1775082086
Does an injective $\mathbb F_9$ vector space homomorphism $\mathbb F_9^5 \to \mathbb F_9^3$ exist?
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No. There isn't even an injective map (of sets) because the sets are finite and the domain has more elements than the codomain.