If $\begin{vmatrix} 2 & 3 & 2 \\ x & x & x \\ 4 & 9 & 1 \end{vmatrix} + 3 = 0$, then the value of $x$ is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $-1$ ##
Given $\begin{vmatrix} 2 & 3 & 2 \\ x & x & x \\ 4 & 9 & 1 \end{vmatrix} + 3 = 0$
On expanding along $R_1$:
$2(x - 9x) - 3(x - 4x) + 2(9x - 4x) + 3 = 0$
$2(-8x) - 3(-3x) + 2(5x) + 3 = 0$
$-16x + 9x + 10x + 3 = 0$
$3x + 3 = 0$
$3x = -3$
$x = -\frac{3}{3}$
$x = -1$