Question: 4 -5 3. The eigenvalues of A = are ) = 13i, and a complex eigenvector associated to 4 + 32 1 = 32 is

4 -5 3. The eigenvalues of A = are ) = 13i, and a complex eigenvector associated to 4 + 32 1 =

(a) What is the complex solution of Y' = AY associated with

4 -5 3. The eigenvalues of A = are ) = 13i, and a complex eigenvector associated to 4 + 32 1 = 32 is . Use this information to answer the following questions. 5 (a) What is the complex solution of Y' = AY associated with the complex eigenvalue and eigenvector given above? (b) Using the complex solution you gave in (a) above, give two linearly independent2- valued solutions of Y' = AY. (c) State with reason whether the origin is a spiral source, a spiral sink or a center for the system Y' = AY.

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