If the system of linear equations,$x+y+z = 6$,$x+2y+3z = 10$,and $3x+2y+\lambda z = \mu$ has more than two solutions,then $\mu-\lambda^{2}$ is equal to

The values of $\lambda$ and $\mu$ for which the system of linear equations $x+y+z=2$,$x+2y+3z=5$,and $x+3y+\lambda z=\mu$ has infinitely many solutions are,respectively:

Let $A = \begin{bmatrix} 12 & 24 & 5 \\ x & 6 & 2 \\ -1 & -2 & 3 \end{bmatrix}$. The value of $x$ for which the matrix $A$ is not invertible is

If the system of equations $kx + y + 2z = 1$,$3x - y - 2z = 2$,and $-2x - 2y - 4z = 3$ has infinitely many solutions,then $k$ is equal to ..........

If the system of equations $\begin{bmatrix} 1 & -2 & 5 \\ 2 & -1 & 1 \\ 11 & -7 & p \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 3 \\ 1 \\ q \end{bmatrix}$ has infinitely many solutions,then:

The set of real values of $\alpha$ for which the system of linear equations
$\begin{aligned}
& x+(\sin \alpha) y+(\cos \alpha) z=0 \\
& x+(\cos \alpha) y+(\sin \alpha) z=0 \\
& -x+(\sin \alpha) y-(\cos \alpha) z=0
\end{aligned}$
has a non-trivial solution is