The integral value of k for which the system of linear equations $kx + y + 2z = 0, ky=x-3z$ and $2x + y + kz = 0$ has a non-zero solution is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2 **
Coefficient matrix:
$\begin{vmatrix}k & 1 & 2\\ -1 & k & 3\\ 2 & 1 & k\end{vmatrix}=0$
Determinant:
$k^3-6k+4=0$
Factorising: $(k-2)(k^2+2k-2)=0$ ⇒ $k=2,\ -1\pm\sqrt{3}$
Integral value of $k$ is 2.