Question

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

• A. 0
• B. 1
• C. -3
• D. 3

Answer 1

Answer: (C)

Let $A=\left[\begin{array}{ccc}1& 2& x\\ 4& -1& 7\\ 2& 4& -6\end{array}\right]$ is a singular matrix
Then, $|A|=0$
$\therefore \left|\begin{array}{ccc}1& 2& x\\ 4& -1& 7\\ 2& 4& -6\end{array}\right|=0$
$\Rightarrow 1[6-28]-2[-24-14]+x[16+2]=0$
$\Rightarrow -22-2\times (-38)+x\times 18=0$
$\Rightarrow -22+76+18x=0$
$\Rightarrow x=-3$