(3 points) Let V, W be finite dimensional vector spaces over F and let T:V→W be a linear map. Recall the isomorphism we constructed in class Φ V
:V→V ∗∗
by sending V to ev v
. Prove that the following diagram commutes ie, that Φ W
∘T=T ∗∗
∘Φ V
(Hint: Recall that T ∗∗
:V ∗∗
→W ∗+
sends a linear functional φ:V ∗
→F to the linear functional φ∘T ∗
:W ∗
→F. That is T ∗∗
φφ)=φ∘T ∗
∈W ∗∗
. You will then evaluate what this is on a linear functional γ∈W ∗
)