# Finding eigenvectors of a 3x3 matrix 2

I am trying to find the eigenvectors of the following 3x3 matrix:

\begin{bmatrix} -9 & 4 & 4 \\ -8 & 3 & 4 \\ -16 & 8 & 7 \\ \end{bmatrix}

The eigenvalues for the matrix are $\lambda_1=3$, $\lambda_2=-1$, $\lambda_3=-1$.

$\lambda_1=3$ :

$$\lambda I_3-A=\begin{bmatrix} (3)+9 & -4 & -4 \\ 8 & (3)-3 & -4 \\ 16 & -8 & (3)-7 \\ \end{bmatrix}=\begin{bmatrix} 12 & -4 & -4 \\ 8 & 0 & -4 \\ 16 & -8 & -4 \\ \end{bmatrix}$$

$$8x-4z=0$$