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A linear map from a five-dimensional space to a three-dimensional space cannot be injective because its rank is at most three, so its nullity is at least two.

Conditions: The domain is five-dimensional.; The codomain is three-dimensional.; The map is linear.

A linear map from a five-dimensional space to a three-dimensional space cannot be injective because its rank is at most three, so its nullity is at least two.

Conditions: The domain is five-dimensional.; The codomain is three-dimensional.; The map is linear.