## Powers and roots of a matrix

Use Jordan normal form and calculate the third power and a square root of the following matrix.

(By a square root consider a matrix whose second power is the given matrix.)

• #### Variant 1

$$\begin{pmatrix} -11 & 30 \\ -10 & 24 \\ \end{pmatrix}$$

• #### Variant 2

$$\begin{pmatrix} 0 & 2 & -2 \\ 1 & -1 & 5 \\ 2 & -4 & 8 \\ \end{pmatrix}$$

• #### Variant 3

$$\begin{pmatrix} 2 & 0 & 0 \\ -4 & 1 & 3 \\ -4 & 0 & 4 \\ \end{pmatrix}$$

• #### Variant 4

$$\begin{pmatrix} 4 & -2 & 0 \\ 0 & 2 & 0 \\ 6 & -5 & 1 \\ \end{pmatrix}$$