The value of the determinant $\left| {\,\begin{array}{*{20}{c}}1&a&{b + c}\\1&b&{c + a}\\1&c&{a + b}\end{array}\,} \right|$is
$a + b + c$
${(a + b + c)^2}$
$0$
$1 + a + b + c$
The existence of the unique solution of the system $x + y + z = \lambda ,$ $5x - y + \mu z = 10$, $2x + 3y - z = 6$ depends on
The system of equations ${x_1} - {x_2} + {x_3} = 2,$ $\,3{x_1} - {x_2} + 2{x_3} = - 6$ and $3{x_1} + {x_2} + {x_3} = - 18$ has
The values of $\alpha$, for which $\left|\begin{array}{ccc}1 & \frac{3}{2} & \alpha+\frac{3}{2} \\ 1 & \frac{1}{3} & \alpha+\frac{1}{3} \\ 2 \alpha+3 & 3 \alpha+1 & 0\end{array}\right|=0$, lie in the interval
The value of the determinant $\left| {\,\begin{array}{*{20}{c}}2&8&4\\{ - 5}&6&{ - 10}\\1&7&2\end{array}\,} \right|$is
Consider the following system of equations : $x+2 y-3 z=a$ ; $2 x+6 y-11 z=b$ ; $x-2 y+7 z=c$ where $a , b$ and $c$ are real constants. Then the system of equations :