A real 3 × 3 matrix A has eigenvalues -.5 , .2 + .3i , \text{and} .2 - .3i , with corresponding eigenvectors
v_{1} = \left [ \begin{matrix} 1 \\ -2 \\ 1 \end{matrix} \right ] , v_{2} = \left [ \begin{matrix} 1+2i \\ 4i \\ 2 \end{matrix} \right ] , \text{and} v_{3} = \left [ \begin{matrix} 1-2i \\ -4i \\ 2 \end{matrix} \right ]
1. Is A diagonalizable as A = PDP^{-1} , using complex matrices?
2. Write the general solution of \acute{x} = Ax using complex eigenfunctions, and then find the general real solution.
3. Describe the shapes of typical trajectories.