The spectral norm of a matrix A c Ross is defined as |4. = max - Ar| : (x| = 1). where [-| is the Euclidean norm on R". (a) Show that (yAr : [x] = 1 and ly] = 1). largest singular value of A. (b) IA : R" + R" and B : R" + R*, then show that IBAL. & IBL. IAL.- (c) II A = [Any, then show that Ajj & AL. for all i.j