The system of equations $x+y+z=6$,$x+2y+5z=9$,$x+5y+\lambda z=\mu$ has no solution if

If the system of equations,$a^2 x - ay = 1 - a$ and $bx + (3 - 2b) y = 3 + a$ possess a unique solution $x = 1, y = 1$,then:

Let $x = \alpha, y = \beta, z = \gamma$ be the unique solution of the system of simultaneous linear equations $2x + 3y - 2z + 4 = 0$, $3x - 4y + 3z + 5 = 0$, and $kx - 2y + z + 3 = 0$. If $\alpha = -2$, then $k =$

If $x = \alpha, y = \beta, z = \gamma$ is the unique solution of the system of equations $5x - 2y + 3z = 0$, $7x + 10y - 8z = 3$ and $2x + 3y - 4z = -4$, then $\beta =$

Let $S$ be the set of all $\lambda \in \mathbb{R}$ for which the system of linear equations
$2x - y + 2z = 2$
$x - 2y + \lambda z = -4$
$x + \lambda y + z = 4$
has no solution. Then the set $S$

The existence of the unique solution of the system of equations $2x + y + z = \beta$,$10x - y + \alpha z = 10$ and $4x + 3y - z = 6$ depends on