If 'a' is non real complex number for | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$\left|\begin{array}{ccc}{a} & {-a^{2}} & {a^{3}} \ {-a^{2}} & {a^{3}} & {a} \ {a^{3}} & {a} & {-a^{2}}\end{array}ight|=0$

Vedclass · Accepted Answer

$1$

Vedclass · Answer

$\left|\begin{array}{ccc}{a} & {-a^{2}} & {a^{3}} \ {-a^{2}} & {a^{3}} & {a} \ {a^{3}} & {a} & {-a^{2}}\end{array}ight|=0$

$\Rightarrow a^{3}(a+1)^{2}\left(a^{2}-a+1ight)^{2}=0$

$ \Rightarrow {m{a}} = 0, - 1, - \omega , - {\omega ^2}$

$\Rightarrow \mathrm{a}=-\omega,-\omega^{2}$  (non real)

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

Similar Questions

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