Let V be a finite-dimensional inner product by T (x)r -(r, y) y for all r e V. space and let y V be a unit vector. Define T: V-V (a) Show that T is linear. (b) Show that T is a projection. (c) Show that T is a self-adjoint. (d) Briefly explain why T is an orthogonal projection. (e) Describe the subspace onto which T projects.