Jordan form - diagonalizable matrices

Task number: 2663

Factorize the following matrix as \(\mathbf R\mathbf J\mathbf R^{-1}\), where \(\mathbf R\) is regular and \(\mathbf J\) is in the Jordan normal form.

  • 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: Hard task
Routine calculation training
Cs translation
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