The system of linear equations $3x - 2y - kz = 10$,$2x - 4y - 2z = 6$,and $x + 2y - z = 5m$ is inconsistent if

Let $M = (a_{ij})$,$i, j \in \{1, 2, 3\}$,be a $3 \times 3$ matrix such that $a_{ij} = 1$ if $j+1$ is divisible by $i$,otherwise $a_{ij} = 0$. Then which of the following statements is (are) true?
$(A)$ $M$ is invertible
$(B)$ There exists a nonzero column matrix $\begin{bmatrix} a_1 \\ a_2 \\ a_3 \end{bmatrix}$ such that $M \begin{bmatrix} a_1 \\ a_2 \\ a_3 \end{bmatrix} = \begin{bmatrix} -a_1 \\ -a_2 \\ -a_3 \end{bmatrix}$
$(C)$ The set $\{X \in \mathbb{R}^3 : MX = 0, X \neq 0\}$ is non-empty,where $0 = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}$
$(D)$ The matrix $(M - 2I)$ is invertible,where $I$ is the $3 \times 3$ identity matrix

The values of $\lambda$ and $\mu$ for which the system of equations $x+y+z=6, x+2y+3z=10, x+2y+\lambda z=\mu$ has infinitely many solutions are

Let the system of equations $x+2y+3z=5$,$2x+3y+z=9$,and $4x+3y+\lambda z=\mu$ have an infinite number of solutions. Then $\lambda+2\mu$ is equal to:

For which of the following ordered pairs $(\mu, \delta)$ is the system of linear equations $x+2y+3z=1$,$3x+4y+5z=\mu$,and $4x+4y+4z=\delta$ inconsistent?

The values of $x, y, z$ in order for the system of equations $3x + y + 2z = 3,$ $2x - 3y - z = -3,$ and $x + 2y + z = 4$ are: