Chapter 5.7, Problem 2PP

A real 3 × 3 matrix A has eigenvalues −.5, .2 + .3i. and .2− ,3i, with corresponding eigenvectors

v₁ = $\left[\begin{array}{l}1\\ -2\\ 1\end{array}\right]$, v₂ = $\left[\begin{array}{l}1+2i\\ 4i\\ 2\end{array}\right]$, and v₃ = $\left[\begin{array}{l}1-2i\\ -4i\\ 2\end{array}\right]$

2. Write the general solution of x′ = Ax using complex eigenfunctions, and then find the general real solution.