How to find the eigenvalues and eigenvector without computation? The given matrix is 
$$
\begin{pmatrix}
2 & 2 & 2 \\
2 & 2 & 2 \\
2 & 2 & 2 \\
\end{pmatrix}
$$
so, how could i find the eigenvalues and eigenvector without computation?
Thank you

Try to solve the following matrix equation, taking into account that your matrix is singular:
$$\begin{pmatrix}2&2&2\\2&2&2\\2&2&2\end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}2(x+y+z)\\2(x+y+z)\\2(x+y+z)\end{pmatrix}=2\begin{pmatrix}x+y+z\\x+y+z\\x+y+z\end{pmatrix}=\lambda\begin{pmatrix}x\\y\\z\end{pmatrix}$$
