The values of $x,y,z$ in order of the system of equations $3x + y + 2z = 3,$ $2x - 3y - z = - 3$, $x + 2y + z = 4,$ are
$2, 1, 5$
$1, 1, 1$
$1, -2, -1$
$1, 2, -1$
If the system of linear equations $x + y + z = 5$ ; $x = 2y + 2z = 6$ ; $x + 3y + \lambda z = u (\lambda \, \mu \in R)$, has infinitely many solutions then the value of $\lambda + \mu $ is
The values of $x $ in the following determinant equation, $\left| {\,\begin{array}{*{20}{c}}{a + x}&{a - x}&{a - x}\\{a - x}&{a + x}&{a - x}\\{a - x}&{a - x}&{a + x}\end{array}\,} \right| = 0$ are
If $\left| {\,\begin{array}{*{20}{c}}{x + 1}&1&1\\2&{x + 2}&2\\3&3&{x + 3}\end{array}\,} \right| = 0,$ then $x$ is
The roots of the equation $\left| {\,\begin{array}{*{20}{c}}0&x&{16}\\x&5&7\\0&9&x\end{array}\,} \right| = 0$ are
Find area of the triangle with vertices at the point given in each of the following: $(2,7),(1,1),(10,8)$