Question: Let L: V W be a linear transformation from a vector space V into a vector space W. The image of a subspace V1

Let L: V → W be a linear transformation from a vector space V into a vector space W. The image of a subspace V1 of V is defined as
L(V1) = {w in W | w = L(v) for some v in V}.
Show that L(V1) is a subspace of V.

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