Let the system of linear equations $x+y+kz=2$; $2x+3y-z=1$; $3x+4y+2z=k$ have infinitely many solutions. Then the system $(k+1)x+(2k-1)y=7$; $(2k+1)x+(k+5)y=10$ has:

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

If $X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}$ is a solution of the system of equations $AX = B$,where $\text{adj } A = \begin{bmatrix} 4 & 2 & 2 \\ -5 & 0 & 5 \\ 1 & -2 & 3 \end{bmatrix}$ and $B = \begin{bmatrix} 4 \\ 0 \\ 2 \end{bmatrix}$,then $|x + y + z|$ is equal to:

Let $\lambda \in R$. The system of linear equations
$2x_{1} - 4x_{2} + \lambda x_{3} = 1$
$x_{1} - 6x_{2} + x_{3} = 2$
$\lambda x_{1} - 10x_{2} + 4x_{3} = 3$
is inconsistent for:

If the system of equations $x + 2y - 3z = 1$,$(k + 3)z = 3$,and $(2k + 1)x + z = 0$ is inconsistent,then the value of $k$ is