Question

If the system of equations $x + ky - z = 0, 3x - ky - z = 0$ and $x - 3y + z = 0$, has non-zero solution, then $k$ is equal to

• A. -1
• B. 0
• C. 1
• D. 2

Answer 1

Answer: (C)

1

Answer 2

The system has non- zero solution, if
$\begin{vmatrix}1&k&-1\\\ 3&-k&-1\\\ 1&-3&1\end{vmatrix} = 0$
$\Rightarrow 1\left(-k -3\right) -k \left(3 + 1\right) -1\left(-9 + k\right) = 0$
$\Rightarrow- 6k + 6 = 0$
$\Rightarrow k = 1$