Question

If $A=\left[\begin{array}{cc}x& x-1\\ 2x& 1\end{array}\right]$ and if $\text{det}A=-9$, then the values of $x$ are

• A. $\frac{3}{2},-3$
• B. $\frac{-2}{3},3$
• C. $\frac{2}{3},3$
• D. $\frac{-3}{2},3$
• E. $\frac{-3}{2},-3$

Answer 1

Answer: (D)

$\frac{-3}{2},3$

Given, $A=\left[\begin{array}{cc}x& x-1\\ 2x& 1\end{array}\right]$, $\text{det}A=-9$
$\Rightarrow \left|A\right|=\left|\begin{array}{cc}x& x-1\\ 2x& 1\end{array}\right|$
$\Rightarrow -9=x-2x(x-1)$
$\Rightarrow -9=x-2x^2+2x$
$\Rightarrow 2x^2-3x-9=0$
$\Rightarrow 2x^2-6x+3x-9=0$
$\Rightarrow 2x(x-3)+3(x-3)=0$
$\Rightarrow (x-3)(2x+3)=0$
$\Rightarrow x=3,-\frac{3}{2}$