Matrices with functions

Task number: 2602

Calculate determinants of the following matrices:

  • Variant 1

    \( \begin{pmatrix} \sin x & \cos x & 1 \\ \sin y & \cos y & 1 \\ \sin z & \cos z & 1 \\ \end{pmatrix} \)

  • Variant 2

    \( \begin{pmatrix} \cos x & \sin x \cos y & \sin x \sin y \\ -\sin x & \cos x \cos y & \cos x \sin y \\ 0 & -\sin y & \cos y \\ \end{pmatrix} \)

  • Variant 3

    \( \begin{pmatrix} 1 & \log_b a & \log_c a \\ \log_a b & 1 & \log_c b \\ \log_a c & \log_b c & 1 \\ \end{pmatrix} \)

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