Question

Is this possible $a\ne 0.\left|\begin{array}{ccc}x+1& x& x\\ x& x+a& x\\ x& x& x+a^2\end{array}\right|=0$ represents a straight line parallel to the y-axis.

• A. True
• B. False

Answer 1

The correct option is A True

$\because$ {$R_1\to R_1-R_2,R_2\to R_2-R_3$}

expand along first row....

$1[\left(a\right)(x+a^2)+a^{2}x]+x\left[a^3\right]=0$

$\Rightarrow x+a^2+ax+a^{2}x=0$

$\Rightarrow x=\frac{-a^2}{a^2+a+1}$

(Represents a straight line parallel to $y-$ axis).