... either a = 0 and b = 0 or b = 0 and a = 0. In the first case 0 = ad + bc = bc and therefore, c = 0; in the second case ad = 0 and, therefore, d = 0. In either case we get a noninvertiblematrix ... believe that they will beof interest to many readers.I assume that the reader is acquainted with main notions of linear algebra:linear space, basis, linear map, the determinant of a matrix. Apart ... The determinant of this system is a Vandermonde determinant. It doesnot vanish and, therefore, n1= ··· = nk= 0. 24.2.2. Theorem. Let A : V → V be a linear operator and W an invariantsubspace,...