Matrices with parameters

Task number: 2600

Deremine determinants of the following real matrices with parameters:

  • Variant 1

    \( \begin{pmatrix} 2 & 2 & -1 & a \\ 2 & -2 & 1 & b \\ 1 & 2 & 2 & c \\ -1 & 2 & -1 & d \\ \end{pmatrix} \)

  • Variant 2

    \(\begin{pmatrix} 0 & b & 1 & 0 \\ a & 0 & 1 & 1 \\ 1 & 1 & 0 & d \\ 0 & 1 & c & 0 \\ \end{pmatrix} \)

  • Variant 3

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

  • Variant 4

    \(\begin{pmatrix} a & 0 & 1 & -1 \\ 0 & b & -1 & 1 \\ 1 & -1 & c & 0 \\ -1 & 1 & 0 & d \\ \end{pmatrix} \)

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
Send comment on task by email