If the system of linear equations $x+y+3 z=0$

$x+3 y+k^{2} z=0$

$3 x+y+3 z=0$

has a non-zero solution $(x, y, z)$ for some $k \in R ,$ then $x +\left(\frac{ y }{ z }\right)$ is equal to

For positive numbers $x,y$ and $z$  the numerical value of the determinant $\left| {\,\begin{array}{*{20}{c}}1&{{{\log }_x}y}&{{{\log }_x}z}\\{{{\log }_y}x}&1&{{{\log }_y}z}\\{{{\log }_z}x}&{{{\log }_z}y}&1\end{array}\,} \right|$is

Evaluate $\left|\begin{array}{rr}2 & 4 \\ -1 & 2\end{array}\right|$

If the system of linear equations  $2 x + y - z =7$ ; $x-3 y+2 z=1$  ; $x +4 y +\delta z = k$, where $\delta, k \in R$  has infinitely many solutions, then $\delta+ k$ is equal to

If $a \ne 6,b,c$ satisfy $\left| {\,\begin{array}{*{20}{c}}a&{2b}&{2c}\\3&b&c\\4&a&b\end{array}\,} \right| = 0,$then $abc = $