Question

If $\left[\begin{array}{ccc}1& 2& x\\ 4& -1& 7\\ 2& 4& 6\end{array}\right]$ is a singular matrix, then $x=$

• A. $0$
• B. $1$
• C. $-3$
• D. $3$

Answer 1

Answer: (C)

$-3$

$\left|\begin{array}{ccc}1& 2& x\\ 4& -1& 7\\ 2& 4& -6\end{array}\right|=0$
$\Rightarrow 1\left|\begin{array}{cc}-1& 7\\ 4& -6\end{array}\right|-2\left|\begin{array}{cc}4& 7\\ 2& -6\end{array}\right|+x\left|\begin{array}{cc}4& -1\\ 2& 4\end{array}\right|=0$
$\Rightarrow (6-28)-2(-24-14)+x(16+2)=0$
$\Rightarrow -22+76+18x=0$
$\Rightarrow 18x=-54$

$\Rightarrow x=-3$