Assume that h: V W is linear. (a) Show that the range space of this map
Question:
(a) Show that the range space of this map {h() | ∈ V} is a subspace of the codomain W.
(b) Show that the null space of this map { ∈ V | h() = W} is a subspace of the domain V.
(c) Show that if U is a subspace of the domain V then its image {h() | ∈ U} is a subspace of the codomain W. This generalizes the first item.
(d) Generalize the second item.
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This will appear as a lemma in the next subsection a The range is nonempty because V is nonempty To ...View the full answer
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