Science:Math Exam Resources/Courses/MATH221/April 2013/Question 09/Hint 1

If you want to avoid the fractions in the matrix $\ A$, you can determine the eigenvalues and eigenvectors of the matrix $\ B=10A$.

The eigenvector of $\ B$ and $\ A$ are the same, while the eigenvalues of $\ B$ are ten times the eigenvalues of $\ A$.