Question

If cofactor of 2x in the determinant $\left|\begin{array}{ccc}x& 1& -2\\ 1& 2x& x-1\\ x-1& x& 0\end{array}\right|$ is zero, then $x$ equals to

• A. 0
• B. 2
• C. 1
• D. -1

Answer 1

The correct option is C 1

Cofactor of $2x=0$

$\Rightarrow C_{22}=0$

$\Rightarrow -1^{(2+2)}\left|\begin{array}{cc}x& -2\\ x-1& 0\end{array}\right|=0$

$\Rightarrow x\times 0-(-2)(x-1)=0$

$\Rightarrow 2(x-1)=0\Rightarrow x=1$