Question: Assume that h: V W is linear. (a) Show that the range space of this map {h() | V} is a subspace

Assume that h: V → W is linear.
(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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