1.4.40 Matrix transformations

Condition: Find the Jordan form of the matrix. \[ A=\left[\begin{array}{cccccc} 2 & 0 & 0 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 & 0 & 0 \\ 1 & -1 & -4 & 0 & 0 & 0 \\ 3 & 2 & 1 & -4 & 0 & 0 \\ -2 & 2 & 5 & 7 & -4 & 0 \\ 4 & 3 & 8 & 6 & 0 & -4 \end{array}\right] \]