Suppose UU is a subspace of VV. Define Γ:L(V/U,W)→L(V,W)\Gamma : \mathcal L(V/U,W) \to \mathcal L(V,W) by

Γ(S)=S∘π.\Gamma(S) = S \circ \pi.
  1. Show that Γ\Gamma is a linear map.
  2. Show that Γ\Gamma is injective
  3. Show that range Γ={T∈L(V,W):Tu=0 for every u∈U}\text{range }\Gamma = \{T \in \mathcal L(V,W) : Tu = 0 \text{ for every }u\in U\}

TODO