Question

If $\left|\begin{array}{ccc}1& 3& 4\\ 1& x-1& 2x+2\\ 2& 5& 9\end{array}\right|=0$, then $x$ is equal to-

• A. $2$
• B. $1.222$
• C. $4$
• D. $0$

Answer 1

Answer: (A)

$2$

Given,

$\left|\begin{array}{ccc}1& 3& 4\\ 1& x-1& 2x+2\\ 2& 5& 9\end{array}\right|=0$

$\Rightarrow 1\cdot \left|\begin{array}{cc}x-1& 2x+2\\ 5& 9\end{array}\right|-3\cdot \left|\begin{array}{cc}1& 2x+2\\ 2& 9\end{array}\right|+4\cdot \left|\begin{array}{cc}1& x-1\\ 2& 5\end{array}\right|=0$

$\Rightarrow 1\cdot (-x-19)-3(-4x+5)+4(-2x+7)=0$

$\Rightarrow 3x-6=0$

$\Rightarrow x=2$