The system of equations $kx + y + z =1$ $x + ky + z = k$ and $x + y + zk = k ^{2}$ has no solution if $k$ is equal to

If the system of linear equations $2x + 2y + 3z = a$ ; $3x – y + 5z = b$ ; $x – 3y + 2z = c$ Where $a, b, c$ are non zero real numbers, has more than one solution, then

Find area of the triangle with vertices at the point given in each of the following: $(2,7),(1,1),(10,8)$

Let $k_1$, $k_2$ be the maximum and minimum values of $k$ for which the system of equations given by

$x + ky = 1$ ; $kx + y = 2$;  $x + y = k$  are consistent then $k_1^2 + k_2^2$ is equal to

The value of $\left| {\begin{array}{*{20}{c}}
1&x&y\\
2&{\sin x + 2x}&{\sin y + 2y}\\
3&{\cos x + 3x}&{\cos y + 3y}
\end{array}} \right|$ is