Question: Let V and W be nite-dimensional vector spaces, V1 be a subspace of V, and T : V > W be linear. Show that T

Let V and W be nite-dimensional vector spaces, V1 be a subspace of V, and T : V > W be linear. Show that T (V1) is a subspace of W. Apply the Rank-Nullity theorem to T|V1 to conclude dim (V1) = dim(N(T) 0 V1) + dim(T(V1)). T|V1 is read \"T restricted to V1\" and means that we change the domain of the transformation T from V to V1

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