How can I find the eigenvalue that is smallest .?
Apply the inverse power method to approximate, for the matrix $A$, the eigenvalue that is smallest in magnitude. Use the given initial vector $x_0$, $k$ iterations, and three-decimal-place accuracy. $$ A = \begin{bmatrix} 4 &1 &0\\ 0 &6 &5\\ 0 &1 &3\end{bmatrix},$$
$$x_0 = \begin{bmatrix}1\\ 1\\ 1\end{bmatrix},$$ $3$ iterations
The eigenvalue smallest in magnitude means the eigenvalue with the smallest absolute value.