CBSE Class 12 Mathematics — Determinants

If $\Delta_1 = \begin{vmatrix}1 & 0 & 0\\0 & 2 & 0\\0 & 0 & 3\end{vmatrix}$ and $\Delta_2 = \begin{vmatrix}0 & 2 & 0\\1 & 0 & 0\\0 & 0 & 6\end{vmatrix}$, then

One of the values of x for which $\begin{vmatrix}\cos x & \sin x\\-\cos x & \sin x\end{vmatrix} = 1$ is

(a) If $A = \begin{bmatrix}0 & 2 & 1\\ -2 & -1 & -2\\ 1 & -1 & 0\end{bmatrix}$, find $A^{-1}$ and use it to solve the following system of equations: $-2y + z = 7$, $2x - y - z = 8$, $x - 2y = 10$. OR (b) If $\begin{bmatrix}3 & -1 & \sin 3x\\ -7 & 4 & \cos 2x\\ -11 & 7 & 2\end{bmatrix}$ is a singular matrix, then find all values of x, where $x \in [0, \pi/2]$.