Evaluate
\(\begin{vmatrix}2&3&-5 \\[0.3em] 7& 1&-2\\[0.3em] -3&4&1\end{vmatrix}\)
Show that
\(\begin{vmatrix}sin10°&-cos10° \\[0.3em] sin80°& cos80°\\[0.3em] \end{vmatrix}\)
Evaluate the determinants:
\(\begin{vmatrix}2&3&7 \\[0.3em] 13& 17&5\\[0.3em] 15&20&12\end{vmatrix}^2\)
Evaluate the determinants:
\(\begin{bmatrix}a+ib &c+id \\[0.3em] -c+id & a-ib \\[0.3em] \end{bmatrix}\)
Evaluate the determinants:
\(\begin{bmatrix}cos\theta &-sin\theta \\[0.3em] sin\theta & cos\theta \\[0.3em] \end{bmatrix}\)