If the trivial solution is the only solution of the system of equations
$x-ky + z=0$
$kx + 3y-kz = 0$
$3x+y-z=0$, then the set of values of k, is
Answer & explanation
Correct answer: option 4
The given system of equations will have trivial solution only, if
$\begin{vmatrix}1&-k&1\\k&3&-k\\3&1&-1\end{vmatrix}≠0$
$⇒-3+k+k(-k + 3k) + (k −9) ≠0$
$⇒2k^2 + 2k-12≠0$
$⇒k^2+k-6≠0$
$⇒k≠-3,2$
Hence, $k∈R - \{2,-3\}$.