We set $A_1 = \left(\begin{array}{ccc} 3 & -2 & 4 \\ -2 & 6 & 2 \\ 4 & 2 & 3 \end{array}\right)$. By observing the first and last column of $A_1$, determine an eigenvector of $A_1$ and the associated eigenvalue $\lambda_1$.
We set $A_1 = \left(\begin{array}{ccc} 3 & -2 & 4 \\ -2 & 6 & 2 \\ 4 & 2 & 3 \end{array}\right)$.
By observing the first and last column of $A_1$, determine an eigenvector of $A_1$ and the associated eigenvalue $\lambda_1$.