If the system of equations $x+4y-z=\lambda$,$7x+9y+\mu z=-3$,and $5x+y+2z=-1$ has infinitely many solutions,then $(2\mu+3\lambda)$ is equal to:

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:

Let the system of linear equations
$-x+2y-9z=7$
$-x+3y-7z=9$
$-2x+y+5z=8$
$-3x+y+13z=\lambda$
has a unique solution $x=\alpha, y=\beta, z=\gamma$. Then the distance of the point $(\alpha, \beta, \gamma)$ from the plane $2x-2y+z=\lambda$ is

If the system of equations
$ 11 x+y+\lambda z=-5 $
$ 2 x+3 y+5 z=3 $
$ 8 x-19 y-39 z=\mu $
has infinitely many solutions,then $ \lambda^4-\mu $ is equal to :

An ordered pair $(\alpha, \beta)$ for which the system of linear equations $(1 + \alpha)x + \beta y + z = 2$; $\alpha x + (1 + \beta)y + z = 3$; $\alpha x + \beta y + 2z = 2$ has a unique solution,is

$A$ manufacturer produces three products $x, y, z$ which he sells in two markets. Annual sales are indicated below:

Market	$x, y, z$
$I$	$10,000, 2,000, 18,000$
$II$	$6,000, 20,000, 8,000$

If unit sale prices of $x, y$ and $z$ are Rs. $2.50$,Rs. $1.50$ and Rs. $1.00$ respectively,find the total revenue in each market with the help of matrix algebra.