The system of equation $2x + λy = 8, λx+8y = 3$ has a unique solution if the value of $λ$ is (are):
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $λ≠±4$
Given system:
$2x + \lambda y = 8$
$\lambda x + 8y = 3$
For a unique solution, determinant of coefficients ≠ 0:
$\begin{vmatrix}2 & \lambda \\ \lambda & 8\end{vmatrix} \ne 0$
$\Rightarrow 16 - \lambda^{2} \ne 0$
$\Rightarrow \lambda^{2} \ne 16$
$\Rightarrow \lambda \ne \pm 4$
Unique solution for $\lambda \ne \pm 4$