Question$\mathbf{1 6}$ to $\mathbf{2 0}$ refer to the vector equation $\mathbf{A} \cdot \mathbf{x}=\lambda \mathbf{x}$. For the coefficient matrix $\mathbf{A}$ given in each case, determine the eigenvalues and an eigenvector corresponding to each eigenvalue: $16 \quad \mathbf{A}=\left(\begin{array}{rrr}2 & 1 & 1 \\ 1 & 3 & 2 \\ -1 & 1 & 2\end{array}\right)$ $17 \mathbf{A}=\left(\begin{array}{lll}1 & 2 & 2 \\ 1 & 3 & 1 \\ 2 & 2 & 1\end{array}\right)$ $18 \quad \mathbf{A}=\left(\begin{array}{rrr}2 & 0 & 1 \\ -1 & 4 & -1 \\ -1 & 2 & 0\end{array}\right)$ $19 \mathbf{A}=\left(\begin{array}{rrr}1 & -4 & -2 \\ 0 & 3 & 1 \\ 1 & 2 & 4\end{array}\right)$ $20 \quad \mathbf{A}=\left(\begin{array}{lll}3 & 0 & 3 \\ 0 & 3 & 3 \\ 2 & 3 & 1\end{array}\right)$