Question: Exercise 1.1. Let c > 0 be a positive real number. Your answers will depend on 0. Consider the matrix M = (g i). (3.)

Exercise 1.1. Let c > 0 be a positive real number. Your answers will depend on 0. Consider the matrix M = (g i). (3.) 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, nd the eigenvectors of M. (e) Sketch the ellipse 63:2 + 4:53; + y2 = 1 for c = 5. l (f By thinking about the eigenvalues as c ) 00, 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

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