Let $\mathrm{A}=\left[a_{ij}\right]$ and $\mathrm{B}=\left[b_{ij}\right]$ be two $3\times 3$ real matrices such that $b_{ij}={\left(3\right)}^{\left(i+j-2\right)}{a}_{ij}$ , where $i,j=\mathrm{1,2},3$ . If the determinant of $\mathrm{B}$  is  $81$,   then determinant of $\mathrm{A}$ i  s

If the system of linear equations,

$x+y+z=6$

$x+2y+3z=10$

$3x+2y+\lambda z=\mu$

has more than two solutions, then $\mu -{\lambda }^2$, is equal to.

The system of linear equations

$\lambda x+2y+2z=5$

$2\lambda x+3y+5z=8$

$4x+\lambda y+6z=10$

has

If for some $\alpha$ and $\beta$ in $R$ , the intersection of the following three planes

$x+4y-2z=1$

$x+7y-5z=\beta$

$x+5y+\alpha z=5$

is a line in $R^3$ , then $\alpha +\beta$ is equal to: