Exercise 3. In a two-dimensional vector space, consider the operator whose 2 2 matrix, in a orthonormal basis l},|2}}, is written: M =L \\/_ J iv2 3 a) Is M Hermitian? Calculate its eigenvalues and eigenvectors (giving their normalized expansion in terms of the l\\, 2}}ba5is) b) Calculate the matrices that represent the projectors onto these eigenvectors. Then verify that they satisfy the orthogonality and closure relations