Q26 / 75 · JEE Main 2020 (09 Jan Shift 2) · Mathematics

The following system of linear equations
$7 x + 6 y - 2 z = 0$
$3 x + 4 y + 2 z = 0$
$x - 2 y - 6 z = 0,$ has

Solution

$|\begin{matrix} 7 & 6 & - 2 \\ 3 & 4 & 2 \\ 1 & - 2 & - 6 \end{matrix}|$

$= 7 (- 20) - 6 (- 20) - 2 (- 10)$

$= - 140 + 120 + 20 = 0$

So infinite non-trivial solution exist
Now equation $(1) + 3$ equation $(3)$
$\Rightarrow 10 x - 20 z = 0$
$\Rightarrow x = 2 z$

Hence, the correct answer is option: 'C'.