Science:Math Exam Resources/Courses/MATH152/April 2022/Question B5 (c)/Hint 1

Recall, again, that solutions to a differential equation of the form ${\textstyle {\frac {d}{dt}}{\vec {y}}(t)=A{\vec {y}}(t)}$ have the form ${\textstyle {\vec {y}}(t)=ce^{\lambda t}{\vec {v}}}$ (the general solution is the sum of multiple of these solutions, one for each eigenvalue). If we want a real valued solution that doesn’t involve sine and cosine, what does this mean for the eigenvalues and eigenvectors?