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In Exercises $9-18$ , construct the general solution of $\mathbf{x}^{\prime}=A \mathbf{x}$ involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories. $$A=\left[\begin{array}{rr}{-3} & {-9} \\ {2} & {3}\end{array}\right]$$

Here, the Eigen values are complex and the real parts of the Eigen values are zero.Therefore, the trajectories are ellipses about the origin.

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 7

Applications to Differential Equations

Vectors

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