The set of all values of $\lambda$ for which the system of linear  $2{x_1} – 2{x_2} + {x_3} = \lambda {x_1}\;,\;2{x_1} – 3{x_2} + 2{x_3} = \lambda {x_2}\;\;,$$\;\; – {x_1} + 2{x_2} = \lambda {x_3}$ has a non-trivial solution

$\left| {\,\begin{array}{*{20}{c}}{11}&{12}&{13}\\{12}&{13}&{14}\\{13}&{14}&{15}\end{array}\,} \right| = $

If $\left| {\begin{array}{*{20}{c}}
{a – b – c}&{2a}&{2a}\\
{2b}&{b – c – a}&{2b}\\
{2c}&{2c}&{c – a – b}
\end{array}} \right|$ $ = \left( {a + b + c} \right)\,{\left( {x + a + b + c} \right)^2}$ , $x   \ne 0$ and $a + b + c \ne 0$, then $x$ is equal to

If $\left| {\,\begin{array}{*{20}{c}}{{x^2} + x}&{x + 1}&{x – 2}\\{2{x^2} + 3x – 1}&{3x}&{3x – 3}\\{{x^2} + 2x + 3}&{2x – 1}&{2x – 1}\end{array}\,} \right| = Ax – 12$, then the value of $A $ is

Find values of ${x},$ if  $\left|\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right|=\left|\begin{array}{ll}x & 3 \\ 2 x & 5\end{array}\right|$