For each of the following linear systems, discuss the nature of the origin and sketch a corresponding phase portrait (including an explicit computation of the eigenvectors in the case of real eigenvalues). If the origin is a saddle point, identify its stable and unstable manifold. 1. [x = 4x - y = 2x + y

Q: 4. Consider the AR(3) model: y, = 0.216y,-3 + ,1e)-WN(0, 1). (a) Find the solutions (roots) of the…

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Q: 4. Consider the linear system of equations i = Ax, where -a A = a +1 2a +1 and a +0 and a # -1 is a…

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Q: . Solve x decomposition. 1 using eigenvector x2 + t, x, = x1 + 2t with initial conditions 1(0) = 2,…

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Q: Consider the matrix A = . Find the eigenvalues and eigenvectors of A.

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Q: 2. Consider the ARMA(1,1) model, (1 – 0.5B)Y = (1– 0.8B)a,. (a) Verify whether it is stationary, or…

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Q: What are the Eigenvalues of the system below: * dx 2x + y dt dy = -X dt О 01 O 1,1 О 1 О 11

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A: Since you have posted a question with multiple subparts, we will solve the first three subparts…