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