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Suppose that the matrix A A has the following eigenvalues and eigenvectors: (1 point) Suppose that...

Suppose that the matrix A A has the following eigenvalues and eigenvectors:(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 2 = 2i with v1 = 2 - 5i and - 12 = -2i wi

(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 2 = 2i with v1 = 2 - 5i and - 12 = -2i with v2 = (2+1) 2 + 5i Write the general real solution for the linear system r' = Ar, in the following forms: A. In eigenvalue/eigenvector form: 0 4 0 t MODE = C1 sin(2t) cos(2) 5 2 4 0 0 t + C2 sin(2t) + cos(2) 2 -5 B. In fundamental matrix form: 4 4 x(t) [CO] Is 4 4 C. As two equations: (write "c1" and "c2" for ci and c2) x(t) = 4 yt) = 4
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= Aro > () The eigenvalues and eigenvectors of A are as follows: 4 d=20 with = 2 -5i and dq=-zi with ů = [216:] We solve (1)to the system Hence for the linear the general solution system rar be x(+) ar tor2 1 = sin (2+) + 0+ e cos (27) [] J - (18 (A. In eigenvalue / eigenvector form: Oit * (*) sin (2) 4 -2 - ([ Cos (27) @ 5 y (+) cos(2+) 0.t e ta sin (24) + ([11 I using

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