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1. Let T be a linear transformation from vector spaces V to W. a. Suppose that...

1. Let T be a linear transformation from vector spaces V to W.

a. Suppose that U is a subspace of V, and let T(U) be the set of all vectors w in W such that T(v) = w for some v in V. Show that T(U) is a subspace of W.

b. Suppose that dimension of U is n. Show that the dimension of T(U) is less than or equal to n.

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