Powers and roots of a matrix

Task number: 2664

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

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

Difficulty level: Moderate task
Routine calculation training
Cs translation
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