Matrices 3 x 3

Task number: 2658

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

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

Difficulty level: Moderate task
Routine calculation training
Cs translation
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