Question

If $\begin{bmatrix}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{bmatrix}$ is a singular matrix, then $x$ is equal to

• A. 0
• B. 1
• C. -3
• D. 3

Answer 1

Answer: (C)

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