Chapter 5.2, Problem 10E

Exercises 9–14 require techniques from Section 3.1. Find the characteristic polynomial of each matrix, using either a cofactor expansion or the special formula for 3 × 3 determinants described prior to Exercises 15–18 in Section 3.1. [Note: Finding the characteristic polynomial of a 3 × 3 matrix is not easy to do with just row' operations, because the variable λ is involved.]

10. $\left[\begin{array}{ccc}0& 3& 1\\ 3& 0& 2\\ 1& 2& 0\end{array}\right]$