The system of equations $x + 2y = 3$ and $2x + 3y = 3$ has

Let $A = \begin{bmatrix} i & -i \\ -i & i \end{bmatrix}$,where $i = \sqrt{-1}$. Then,the system of linear equations $A^{8} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 8 \\ 64 \end{bmatrix}$ has :

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

For the system of linear equations:
$x - 2y = 1, x - y + kz = -2, ky + 4z = 6, k \in R$
Consider the following statements:
$(A)$ The system has a unique solution if $k \neq 2, k \neq -2$.
$(B)$ The system has a unique solution if $k = -2$.
$(C)$ The system has a unique solution if $k = 2$.
$(D)$ The system has no solution if $k = 2$.
$(E)$ The system has an infinite number of solutions if $k \neq -2$.
Which of the following statements are correct?

If the system of equations
$2x + 7y + \lambda z = 3$
$3x + 2y + 5z = 4$
$x + \mu y + 32z = -1$
has infinitely many solutions,then $(\lambda - \mu)$ is equal to

If ${a_1}x + {b_1}y + {c_1}z = 0, {a_2}x + {b_2}y + {c_2}z = 0, {a_3}x + {b_3}y + {c_3}z = 0$ and $\left| \begin{matrix} {a_1} & {b_1} & {c_1} \\ {a_2} & {b_2} & {c_2} \\ {a_3} & {b_3} & {c_3} \end{matrix} \right| = 0$,then the given system has