Question

lf $\left|\begin{array}{ccc}1& 2& x\\ 4& -1& 7\\ 2& 4& -6\end{array}\right|$ is a singular matrix, then $x$ is equal to

• A. $0$
• B. $1$
• C. $-3$
• D. $3$

Answer 1

Answer: (C)

$-3$

Given $A=\left|\begin{array}{ccc}1& 2& x\\ 4& -1& 7\\ 2& 4& -6\end{array}\right|$ is a singular matrix

So, $detA=0$

$\Rightarrow 1(6-28)-2(-24-14)+x(16+2)=0$

$\Rightarrow -22+76+18x=0$

$\Rightarrow 18x=-54$

$\therefore x=-3$