Question

If $A=\left[\begin{array}{ccc}2& 1& -1\\ 4& x& 6\\ 0& 1& 3\end{array}\right]$ is a singular matrix, then the value of $x$ is

[1 mark]

• A. $4$
• B. $\frac{14}{3}$
• C. $5$
• D. $\frac{11}{3}$

Answer 1

The correct option is B $\frac{14}{3}$

$A=\left[\begin{array}{ccc}2& 1& -1\\ 4& x& 6\\ 0& 1& 3\end{array}\right]$
Since matrix is singular,
$\therefore |A|=0$
$\Rightarrow \left|\begin{array}{ccc}2& 1& -1\\ 4& x& 6\\ 0& 1& 3\end{array}\right|=0$

Expanding along $R_3,$
$-(12+4)+3(2x-4)=0$
$\Rightarrow 6x-28=0$
$\Rightarrow x=\frac{14}{3}$