Matrices 3 x 3

Determine eigenvalues and the corresponding eigenvectors for the following matrix over the field $$\mathbb C$$. Decide whether this matrix is diagonalizable:

• Variant 1

$$\begin{pmatrix} 2 & -1 & 2 \\ 5 & -3 & 3 \\ -1 & 0 & -2 \\ \end{pmatrix}$$

• Variant 2

$$\begin{pmatrix} 2 & -1 & -1 \\ 0 & -1 & 0 \\ 0 & 2 & 1 \\ \end{pmatrix}$$

• Variant 3

$$\begin{pmatrix} 1 & -1 & 0 \\ 0 & 1 & -4 \\ -1 & 0 & 4 \\ \end{pmatrix}$$