If $x=\alpha, y=\beta, z=\gamma$ is the solution of the system of equations $2x+3y+z=-1$,$3x+y+z=4$,and $x-3y-2z=1$,then the value of $\beta$ is:

Consider the following system of equations in matrix form $\begin{bmatrix} 1 \\ 2 \\ \lambda \end{bmatrix} \begin{bmatrix} 1 & 2 & \lambda \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = 0$. Then which one of the following statements is true?

The system of equations $2x + 6y = -11$,$6x + 20y - 6z = -3$ and $6y - 18z = -1$ are

If $(x, y, z)=(\alpha, \beta, \gamma)$ is the unique solution of the system of simultaneous linear equations $3x - 4y + z + 7 = 0$,$2x + 3y - z = 10$,and $x - 2y - 3z = 3$,then $\alpha = $

Let $A$ and $B$ be two $3 \times 3$ non-zero real matrices such that $AB$ is a zero matrix. Then:

The number of solutions of the equations $x + y - z = 0$,$3x - y - z = 0$,and $x - 3y + z = 0$ is