Examine the consistency of the system of equations: $5x - y + 4z = 5$,$2x + 3y + 5z = 2$,and $5x - 2y + 6z = -1$.

The number of solutions of the system of equations $2x + y - z = 7$,$x - 3y + 2z = 1$,and $x + 4y - 3z = 5$ 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.

For the system of equations $x+y+z=6$,$x+2y+\alpha z=10$,and $x+3y+5z=\beta$,which one of the following is $NOT$ true?

The system of equations $3x + 2y + z = 6$, $3x + 4y + 3z = 14$ and $6x + 10y + 8z = a$ has an infinite number of solutions if $a$ is equal to

If $3X + 2Y = I$ and $2X - Y = O$,where $I$ and $O$ are unit and null matrices of order $3$ respectively,then