Find values of $x$ for which $\left|\begin{array}{ll}3 & x \\ x & 1\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right|$

Find equation of line joining $(3,1)$ and $(9,3)$ using determinants

If the system of equations

$x+y+z=2$

$2 x+4 y-z=6$

$3 x+2 y+\lambda z=\mu$ has infinitely many solutions, then 

If $a$, $b$, $c$, $d$, $e$, $f$ are in $G.P$., then the value of $\left| {\begin{array}{*{20}{c}}
  {{a^2}}&{{d^2}}&x \\ 
  {{b^2}}&{{e^2}}&y \\ 
  {{c^2}}&{{f^2}}&z 
\end{array}} \right|$ depends on

$\left| {\,\begin{array}{*{20}{c}}1&a&b\\{ - a}&1&c\\{ - b}&{ - c}&1\end{array}\,} \right| = $

Evaluate $\Delta=\left|\begin{array}{lll}3 & 2 & 3 \\ 2 & 2 & 3 \\ 3 & 2 & 3\end{array}\right|$