Matrices of order 4

Task number: 2597

Calculate determinants of the following real matrices:

  • Variant 1

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

  • Variant 2

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

  • Variant 3

    \(\begin{pmatrix} -1 & -2 & 3 & -1 \\ 2 & 4 & -3 & 1 \\ 1 & 2 & -2 & -1 \\ -2 & -1 & 1 & -2 \\ \end{pmatrix} \)

  • Variant 4

    \(\begin{pmatrix} -2 & 1 & 1 & 1 \\ 1 & 2 & -1 & -2 \\ 1 & -1 & 1 & 1 \\ 1 & 2 & 1 & -2 \\ \end{pmatrix} \)

  • Variant 5

    \(\begin{pmatrix} 1 & 2 & 3 & 4 \\ 2 & 1 & 0 & 3 \\ 3 & 0 & 1 & 2 \\ 4 & 3 & 2 & 1 \\ \end{pmatrix} \)

  • Variant 6

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

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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