Suppose that $\displaystyle {A}$ = $\displaystyle {\left(\begin{array}{ccc} {0}&{0}&-{2}\\{0}&{1}&{0}\\{1}&{0}&{3}\end{array}\right)}$. Find the eigenvalues of $\displaystyle {A}$, i.e. the $\displaystyle \lambda$ which satisfies $\displaystyle {\det}{\left|{A}-\lambda{I}_{{3}}\right|}={0}$.

The eigenvalues of $\displaystyle {A}$ is listed as follows in order from biggest to smallest:
$\displaystyle \lambda_{{1}}=$Preview Question 6 Part 1 of 3  
$\displaystyle \lambda_{{2}}=$Preview Question 6 Part 2 of 3  
$\displaystyle \lambda_{{3}}=$Preview Question 6 Part 3 of 3