If the system of linear equations

$2 x+y-z=3$

$x-y-z=\alpha$

$3 x+3 y+\beta z=3$

has infinitely many solution, then $\alpha+\beta-\alpha \beta$ is equal to .... .

The value of $'a'$ for which the system of equation  $a^3x + (a + 1)^3y + (a + 2)^3 z = 0$ ; $ax + (a + 1)y + (a + 2)z = 0$ ; $x + y + z = 0$  has a non-zero solution is :-

The following system of linear equations  $7 x+6 y-2 z=0$ ; $3 x+4 y+2 z=0$ ; ${x}-2{y}-6{z}=0,$ has

If the system of equations $x - ky - z = 0$, $kx - y - z = 0$ and $x + y - z = 0$ has a non zero solution, then the possible value of k are

If $A=\left[\begin{array}{lll}1 & 1 & -2 \\ 2 & 1 & -3 \\ 5 & 4 & -9\end{array}\right],$ find $|A|$.

If the system of equations

$x-2 y+3 z=9$

$2 x+y+z=b$

$x-7 y+a z=24$

has infinitely many solutions, then $a - b$ is equal to