Let $\lambda, \mu \in R$. If the system of equations
$3x + 5y + \lambda z = 3$
$7x + 11y - 9z = 2$
$97x + 155y - 189z = \mu$
has infinitely many solutions,then $\mu + 2\lambda$ is equal to :

Solve the system of equations $2x + 5y = 1$ and $3x + 2y = 7$.

The system of equations $x + ky - z = 0$,$3x - ky - z = 0$,and $x - 3y + z = 0$ has a non-zero solution for $k =$

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?

Consider the following system of equations: $x+2y-3z=a$,$2x+6y-11z=b$,and $x-2y+7z=c$,where $a, b$,and $c$ are real constants. Then the system of equations:

Consider the following system of equations in matrix form $\begin{bmatrix} 1 \\ 2 \\ \lambda \end{bmatrix} \begin{bmatrix} 1 & 2 & \lambda \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = 0$. Then which one of the following statements is true?