Problem 2. For any matrix A E M,(F), show that (Ar, y) = (x , A*y) for all a, y € F". Use this to show that R(LA-)+ = N(LA). %3D Problem 3. Let V be a finite-dimensional inner product space, and let W...

Plz solve 2

Extracted text: Problem 2. For any matrix A E M,(F), show that (Ar, y) = (x , A*y) for all a, y € F". Use this to show that R(LA-)+ = N(LA). %3D Problem 3. Let V be a finite-dimensional inner product space, and let W C V be a subspace. Show that (W-)- = W.