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

The value of $p$ and $q$ is that system of equations $2 x+p y+6 z=8, x+2 y+q z=5$ and $x+y+3 z=4$ may have no solution are

$A$ is the set of all matrices of order 3 with entries 0 or 1 only. $B$ is the subset of $A$ consisting of all matrices with determinant value 1 . If $C$ is the subset of $A$ consisting of all matrices with determinant value -1 , then

Consider the matrices $A=\left[\begin{array}{ccc}x & y & 0 \\ -3 & 1 & 2 \\ 1 & -2 & z\end{array}\right]$ and $B=\left[\begin{array}{ccc}1 & -2 & -2 \\ 2 & 0 & 1 \\ 2 & 1 & 0\end{array}\right]$

If the cofactors of the elements $z, 1$ in 3rd row and $x$ of $A$ are $9,4,3$, respectively then $A B=$