Consider the system (3) = (1 a21 azz a) Show that the eigenvalues of the coefficient...

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Consider the system (3) = (₂1 a21 azz a) Show that the eigenvalues of the coefficient matrix are pure imaginary if and only if a11 + a22 = 0, 911922-a12a21 > 0 (ii) b) The trajectories of the system can be found by converting the system into a single equation: dy dy/dt_a₂₁x+azzy dx dx/da₁x+any Use the first of Eqs (ii) to show that Eqs (iii) is exact c) By integrating Eq (iii) show that a21x² + 2a22xy-a12y² = k, (iv) Where k is a constant. Use equation (ii) to conclude the graph of Eq (iv) is always an ellipse. Hint: What is the discriminant of the quadratic form in Eq (iv)? (iii) Consider the system (3) = (₂1 a21 azz a) Show that the eigenvalues of the coefficient matrix are pure imaginary if and only if a11 + a22 = 0, 911922-a12a21 > 0 (ii) b) The trajectories of the system can be found by converting the system into a single equation: dy dy/dt_a₂₁x+azzy dx dx/da₁x+any Use the first of Eqs (ii) to show that Eqs (iii) is exact c) By integrating Eq (iii) show that a21x² + 2a22xy-a12y² = k, (iv) Where k is a constant. Use equation (ii) to conclude the graph of Eq (iv) is always an ellipse. Hint: What is the discriminant of the quadratic form in Eq (iv)? (iii)

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Step Given parameters post 4 The coefficient malsix A is expressed as A a dhe 7 the eigen value 21 2... View the full answer