If the equations x = ay + z, y = az + x and z = ax + y are consistent having non-trivial solution, then
Answer & explanation
Correct answer: option 4
$\Delta=\left|\begin{array}{ccc}1 & -a & -1 \\ -1 & 1 & -a \\ -a & -1 & 1\end{array}\right|=0$
⇒ a3 – 3a = 0
Hence (4) is the correct answer.