Let T : V → W be a surjective linear map. For a subspace U ⊆ V, define the restriction T|u ∈ L (U, W) by T|u (u) = T (u) . Prove that there exists a subspace U of V such that T|u is an isomorphism. (Cation: this is a slightly different meaning of the word restriction than we will be using in class this week, becuase only the domain has changed.)