Q. If the system of equations $x + ky - \mathcal{z} = 0,\ 3x - ky - \mathcal{z} = 0\ and\ x - 3y + \mathcal{z} = 0$ has non-zero solution then $k$ is equal to
A) $- 1$
B) 0
C) 1
D) 2
Explanation
(c)
It has a non-zero solution, if$\left| \begin{matrix}
1 & k & - 1 \\
3 & - k & - 1 \\
1 & - 3 & 1
\end{matrix} \right| = 0$
$\Rightarrow 1( - k - 3) - k(3 + 1) - 1( - 9 + k) = 0$
$\Rightarrow \ - 6k + 6 = 0$
$\Rightarrow k = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.