Find the eigenvalues and one corresponding eigenvector for each of the eigenvalues of the following matrix:\\
$A = \begin{bmatrix} 4 & 2 & -4 \\ 0 & -2 & 0 \\ 1 & 0 & 9 \end{bmatrix}$ \\
$\lambda_1 = \Box$, one corresponding eigenvector is: $\vec{v}_1 = \begin{bmatrix} \Box \\ \Box \\ \Box \end{bmatrix}$ \\
and \\
$\lambda_2 = \Box$, one corresponding eigenvector is: $\vec{v}_2 = \begin{bmatrix} \Box \\ \Box \\ \Box \end{bmatrix}$ \\
and \\
$\lambda_3 = \Box$, one corresponding eigenvector is: $\vec{v}_3 = \begin{bmatrix} \Box \\ \Box \\ \Box \end{bmatrix}$
