If $x=\alpha, y=\beta, z=\gamma$ is the solution for the system of equations:
$\begin{aligned} 2x-y+8z &= 13 \\ 3x+4y+5z &= 18 \\ 5x-2y+7z &= 20 \end{aligned}$
then $\alpha\beta+\beta\gamma+\gamma\alpha=$

If for $AX = B,$ $B = \begin{bmatrix} 9 \\ 52 \\ 0 \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} 3 & -\frac{1}{2} & -\frac{1}{2} \\ -4 & \frac{3}{4} & \frac{5}{4} \\ 2 & -\frac{1}{4} & -\frac{3}{4} \end{bmatrix},$ then $X$ is equal to

If the system of equations $2x + py + 6z = 8$,$x + 2y + qz = 5$,and $x + y + 3z = 4$ has infinitely many solutions,then $p=$

The system of equations $x + 3y + 7 = 0$, $3x + 10y - 3z + 18 = 0$ and $3y - 9z + 2 = 0$ has

The system $2x + 3y + z = 5$,$3x + y + 5z = 7$ and $x + 4y - 2z = 3$ has

If the system of equations
$2x + y - z = 5$
$2x - 5y + \lambda z = \mu$
$x + 2y - 5z = 7$
has infinitely many solutions,then $(\lambda + \mu)^2 + (\lambda - \mu)^2$ is equal to