Question: Let V be a finite-dimensional vector space over a field F and let K V be a subspace. A linear functional l : V F

Let V be a finite-dimensional vector space over a field F and let K V be a subspace. A linear functional l : V F can be restricted to a linear functional l|K : K F , so we have a function R : V K which it's easy to see is linear.

(a)Show that R is surjective.

(b)Show that kerR is canonically isomorphic to (V/K) .

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