Q. 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
Explanation
(c)
Since, $A$ is a singular matrix
$\therefore$|$A$|=0
$\Rightarrow \begin{bmatrix}
1 & 2 & x \\
4 & - 1 & 7 \\
2 & 4 & - 6
\end{bmatrix} = 0$
$\Rightarrow 1(6 - 28) - 2( - 24 - 14) + x\lbrack 16 + 2\rbrack = 0$
$\Rightarrow$ $- 22 + 76 + 18x = 0 \Rightarrow x = - 3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.