Let V, W be finite dimensional vector spaces over F and let T: VW be a linear map. Recall the isomorphism V** by sending v to Φv:V → ev. Prove that the following diagram commutes V T W Φρ Φw → V** → W** O ie, that w o T = T** ○ Þy (Hint: Recall that T** : V** → W** sends a linear functional 4: V* → F to the linear functional yoT* : W* → F. That is T** (y) = y0T* € W**. You will then evaluate what this is on a linear functional y € W* )

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