If $'a'$ is non real complex number for which system of equations $ax -a^2y + a^3z$ = $0$ , $-a^2x + a^3y + az$ = $0$ and $a^3x + ay -a^2z$ = $0$ has non trivial solutions, then $|a|$ is
$0$
$1$
$\sqrt3 $
$2$
The values of $\mathrm{m}, \mathrm{n}$, for which the system of equations
$ x+y+z=4 $
$ 2 x+5 y+5 z=17 $
$ x+2 y+m z=n$
has infinitely many solutions, satisfy the equation :
Find area of the triangle with vertices at the point given in each of the following: $(2,7),(1,1),(10,8)$
For all values of $A,B,C$ and $P,Q,R$, the value of $\left| {\,\begin{array}{*{20}{c}}{\cos (A - P)}&{\cos (A - Q)}&{\cos (A - R)}\\{\cos (B - P)}&{\cos (B - Q)}&{\cos (B - R)}\\{\cos (C - P)}&{\cos (C - Q)}&{\cos (C - R)}\end{array}\,} \right|$ is
If the system of linear equations $x-2 y+z=-4 $ ; $2 x+\alpha y+3 z=5 $ ; $3 x-y+\beta z=3$ has infinitely many solutions, then $12 \alpha+13 \beta$ is equal to
If $-9 $ is a root of the equation $\left| {\,\begin{array}{*{20}{c}}x&3&7\\2&x&2\\7&6&x\end{array}\,} \right| = 0$ then the other two roots are