If the system of equations $x+y+z=2$,$2x+4y-z=6$,and $3x+2y+\lambda z=\mu$ has infinitely many solutions,then:

If the system $\begin{bmatrix} 2 & 8 \\ 3 & 7 \end{bmatrix} \begin{bmatrix} a \\ b \end{bmatrix} = k \begin{bmatrix} a \\ b \end{bmatrix}$ has a non-trivial solution,then the positive value of $k$ and a solution of the system for that value of $k$ are:

If the system of linear equations: $x + y + z = 6, x + 2y + 5z = 10, 2x + 3y + \lambda z = \mu$ has infinitely many solutions,then the value of $\lambda + \mu$ equals:

Consider the simultaneous linear equations $\beta x + \alpha y - z = -1$,$3x - \beta y + \alpha z = 0$,and $\alpha x + \beta y + z = 1$. In the usual notation used in Cramer's rule,given that $\frac{\Delta_1}{\Delta} = -1$,$\frac{\Delta_2}{\Delta} = 1$,and $\frac{\Delta_3}{\Delta} = 2$,then $(\alpha, \beta) = $

Let the system of equations $x+5y-z=1$,$4x+3y-3z=7$,$24x+y+\lambda z=\mu$,where $\lambda, \mu \in R$,have infinitely many solutions. Then the number of solutions of this system,if $x, y, z$ are integers and satisfy $7 \leq x+y+z \leq 77$,is

The number of real values of $\alpha$ for which the system of equations
$x+3y+5z=\alpha x$
$5x+y+3z=\alpha y$
$3x+5y+z=\alpha z$
has infinite number of solutions is