(a) Show that the Euclidean norm of a vector v is given by a formula similar to that for the matrix norm: ||v|| = max_x notequalto 0 x middot v/||x||, or equivalently ||v|| = max_x: ||x|| = 1 x middot v by showing that the max on the left side is both greaterthanorequalto and lessthanorequalto the norm ||v|| on the right. (b) Show that the matrix norm of A is given by formula ||A|| = max_x, y notequalto 0 x middot Ay/||x|| ||y|| or equivalently ||A|| = max_x,y: ||x||=||y||=1 x middot Ay (c) Use the formula in the previous part and the fact that for any matrix A, x middot Ay = (A^T X) middot y to show that ||A|| = ||A^T|| for any matrix. Verify this formula using MATLAB/Octave for some randomly chosen (not necessarily square) matrices