If the system of equations $x + y + z = 6$,$x + 2y + 3z = 10$,and $x + 2y + \lambda z = 0$ has a unique solution,then $\lambda$ is not equal to:

If the system of linear equations $x_1 + 2x_2 + 3x_3 = 6$,$x_1 + 3x_2 + 5x_3 = 9$,and $2x_1 + 5x_2 + ax_3 = b$ is consistent and has an infinite number of solutions,then:

The value of $\lambda$ such that the system of equations $2x-y-2z=2$,$x-2y+z=-4$,and $x+y+\lambda z=4$ has no solution,is:

For how many values of $k$ does the system of linear equations $(k + 1)x + 8y = 4k$ and $kx + (k + 3)y = 3k - 1$ have no solutions?

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 = $

If the system of linear equations $x+y+3z=0$,$x+3y+k^{2}z=0$,and $3x+y+3z=0$ has a non-zero solution $(x, y, z)$ for some $k \in R$,then $x + (y/z)$ is equal to