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Let T:V→W be a linear transformation and U be a subspace of V. Let T(U)T(U) denote...

Let T:V→W be a linear transformation and U be a subspace of V. Let T(U)T(U) denote the image of U under T (i.e., T(U)={T(u⃗ ):u⃗ ∈U}). Prove that T(U) is a subspace of W

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