Find the eigenvalues of $A$, given that $A = \left[\begin{array}{ccc} 5 &-5 &-14\cr -4 &6 &14\cr 2 &-5 &-11 \end{array}\right]$

and its eigenvectors are $v_1 = \left[\begin{array}{c} -1\cr 1\cr -1 \end{array}\right], v_2 = \left[\begin{array}{c} -1\cr 2\cr -1 \end{array}\right]$ and $v_3 = \left[\begin{array}{c} 2\cr -2\cr 1 \end{array}\right]$.

The corresponding eigenvalues are $\lambda_1 =$, $\lambda_2 =$, and $\lambda_2 =$.