Let c> 0 be a positive real number. Your answers will depend on c. Consider the matrix M = (21) (a) Find the characteristic polynomial of M. (b) Find the eigenvalues of M. (c) For which values of c are both eigenvalues positive? (d) If c= 5, find the eigenvectors of M. (e) Sketch the ellipse cr² + 4xy + y² = 1 for c = 5. (f) By thinking about the eigenvalues as c→ [infinity]o, can you describe (roughly) what happens to the shape of this ellipse as c increases? 2 marks 2 marks 2 marks 2 marks 1 marks. 1 marks