If the system of simultaneous linear equations $x+\lambda y-2 z=1, x-y+\lambda z=2$ and $x-2 y+3 z=3$ is inconsistent for $\lambda=\lambda_1$ and $\lambda_2$, then $\lambda_1+\lambda_2=$

The system of linear equation $(\sin \theta) x+y-2 z=0$, $2 x-y+(\cos \theta) z=0$ and $-3 x+(\sec \theta) y+3 z=0$, where $\theta \neq(2 n+1) \frac{\pi}{2}$, has non-trivial solution for

If $A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$, then $\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A))$

The sum of all the roots of the equation

$\left|\begin{array}{ccc}x & -3 & 2 \\ -1 & -2 & (x-1) \\ 1 & (x-2) & 3\end{array}\right|=0$ is