Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 04 (b)/Statement

A model of love affairs is described by the following system of differential equations

${\begin{aligned}R'&=R+4J,\\J'&=-2R-3J,\end{aligned}}$

where $R(t)$ and $J(t)$ are, respectively, Romeo’s and Juliet’s amount of love for each other at time $t$.

(b) The eigenvalues of $A$ are $\lambda =-1\pm 2i$. Find the eigenvectors of the matrix with these eigenvalues.