5.18 Let X and Y be finite-dimensional pre-Hilbert spaces and let A: XY be a linear operator. Show that there exists a uniquely determined linear operator A* YX with the property (Ax, y) = (x, A* y)x for all x x and y Є Y. Use this result to formulate and prove a generalization of Theorem 5.9 for the minimization of ||Axy|| + a||x||| .