Find the eigenvalues and eigenvectors of the following matrix: [[A]=left[begin{array}{cc}8 & -1 -4 & 4end{array} ight]] [[[A]-lambda[I]] vec{X}=overrightarrow{0}] where (lambda) is the eigenvalue and (vec{X})

Find the eigenvalues and eigenvectors of the following matrix:

\[[A]=\left[\begin{array}{cc}8 & -1 \\-4 & 4\end{array}\right]\]

\[[[A]-\lambda[I]] \vec{X}=\overrightarrow{0}\]

where \(\lambda\) is the eigenvalue and \(\vec{X}\) is the eigenvector.