The value of the determinant $\left| {\,\begin{array}{*{20}{c}}2&8&4\\{ – 5}&6&{ – 10}\\1&7&2\end{array}\,} \right|$is

The number of solutions of the equations $x + 4y – z = 0,$ $3x – 4y – z = 0,\,x – 3y + z = 0$ is

$\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{1 + x}&1\\1&1&{1 + y}\end{array}\,} \right| = $

If $\left| {\,\begin{array}{*{20}{c}}{{x^2} + x}&{x + 1}&{x – 2}\\{2{x^2} + 3x – 1}&{3x}&{3x – 3}\\{{x^2} + 2x + 3}&{2x – 1}&{2x – 1}\end{array}\,} \right| = Ax – 12$, then the value of $A $ is

If the system of linear equations  $x-2 y+z=-4 $   ;  $2 x+\alpha y+3 z=5 $  ;  $3 x-y+\beta z=3$ has infinitely many solutions, then $12 \alpha+13 \beta$ is equal to