$\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{{\omega ^2}}&\omega \\1&\omega &{{\omega ^2}}\end{array}\,} \right| = $

If $ 5$  is one root of the equation $\left| {\,\begin{array}{*{20}{c}}x&3&7\\2&x&{ – 2}\\7&8&x\end{array}\,} \right| = 0$, then other two roots of the equation are

If $\alpha \neq \mathrm{a}, \beta \neq \mathrm{b}, \gamma \neq \mathrm{c}$ and $\left|\begin{array}{lll}\alpha & \mathrm{b} & \mathrm{c} \\ \mathrm{a} & \beta & \mathrm{c} \\ \mathrm{a} & \mathrm{b} & \gamma\end{array}\right|=0$,then $\frac{a}{\alpha-a}+\frac{b}{\beta-b}+\frac{\gamma}{\gamma-c}$ is equal to :

If the system of equations, $x + 2y – 3z = 1$, $(k + 3)z = 3,$ $(2k + 1)x + z = 0$is inconsistent, then the value of $ k$  is

If the system of equations, $a^2 x – ay = 1 – a$ & $bx + (3 – 2b) y = 3 + a$ possess a unique solution $x = 1, y = 1$ then :