If $A=\left[\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right]$ and $\alpha A^2+\beta A=2 I$ for some $\alpha, \beta \in R$, then $\alpha+\beta=$

The system of equations $$ x+2 y+3 z=6, x+3 y+5 z=9 \text {, } $$ $2 x+5 y+a z=12$ has no solution when $a=$

If $ \alpha, \beta, \gamma $ are the roots of $ \begin{bmatrix} 1 & -x & -2 \\ -2 & 4 & -x \\ -2 & 1 & -x \end{bmatrix} = 0 $, then $ \alpha \beta + \beta \gamma + \gamma \alpha = $

If the determinant of a 3rd order matrix $ A $ is $ K $, then the sum of the determinants of the matrices $ A^4 $ and $ (A - A^4) $ is