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For the matrix S given by S = [54 54i ' a) Find the determinant of S = |S|. (1 mark) b) Find the inverse of S, S". (1 marks) c) Determine the eigenvalue (A1: A2) and eigenvectors for S". (3 marks) (1) Determine the half lengths of the axes of the ellipse. (3 marks) e} In which direction does the major axis lie? (1 mark} f) In which direction does the minor axis lie? (1 mark)