Question

The characteristic equation associated with the matrix $\left[\begin{matrix}0& 0& 3\\ 1& 0& 2\\ 0& 1& 1\end{matrix}\right]$ is

• A. $\lambda^{3} - \lambda^{2} - 2\lambda - 3 = 0$
• B. $\lambda^{3} - \lambda^{2} + 2\lambda - 3 = 0$
• C. $\lambda^{3} - \lambda^{2} - 3\lambda - 3 = 0$
• D. $\lambda^{3} - \lambda^{2} + 3\lambda - 3 = 0$

Hint:

For a $3 \times 3$ matrix, the equation is $\lambda^3 - Tr(A)\lambda^2 + (S_{11}+S_{22}+S_{33})\lambda - \det(A) = 0$, where $S_{ii}$ are principal minors.

Answer 1

The Correct Option is A