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Question: 5 given a system of homogenous linear differential equations dr...

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5. Given a system of homogenous linear differential equations dr dy-2x-2 z = 0 dt dz dt (a) Write the system of equations in the form dX AX dt where X =| y | and identify the matrix A. (15 marks) (b) Show that is an eigenvector of the matrix A found in (a). State the corresponding eigenvalue (35 marks) (c). Find two other eigenvectors and state the corresponding eigenvalues (30 marks) (d) Hence write down the general solution of the svstem as given in
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