If the system of equations
$x-2y+3z=9$
$2x+y+z=b$
$x-7y+az=24$
has infinitely many solutions,then $a-b$ is equal to

If the system of equations $x + ay = 0,$ $az + y = 0$ and $ax + z = 0$ has infinite solutions,then the value of $a$ is

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 the system of simultaneous linear equations $3x - 4y + kz + 13 = 0$,$x + 2y - z - 9 = 0$,and $kx - y + 3z + 7 = 0$ has a unique solution $x = \alpha, y = \beta, z = \gamma$ for $k \neq m$ and $2\beta - \gamma = 8$,then $\alpha + m =$

$A$ and $C$ lie in $\left[0, \frac{\pi}{2}\right)$ and $B$ lies in $[0, 2\pi]$. If $\tan A + 3 \cos B + 6 \sin C = 1$; $3 \tan A + \cos B + 4 \sin C = 4$; $5 \tan A + 3 \cos B - 8 \sin C = -2$,then $B - 2A - C =$

If $A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{bmatrix}$,find $A^{-1}$. Using $A^{-1}$,solve the system of equations: $2x - 3y + 5z = 11$,$3x + 2y - 4z = -5$,and $x + y - 2z = -3$.