Chapter 5.2, Problem 12E

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.]

12. $\left[\begin{array}{ccc}-1& 0& 1\\ -3& 4& 1\\ 0& 0& 2\end{array}\right]$