Question

The system of equations $\lambda x + y + z = 0,$ $- x + \lambda y + z = 0,$ $- x - y + \lambda z = 0$, will have a non zero solution if real values of $\lambda$are given by.

• A. 0
• B. 1
• C. 3
• D. $\sqrt{3}$

Answer 1

Answer: (A)

0

Answer 2

Accordingly,

\lambda & 1 & 1 \\ - 1 & \lambda & 1 \\ - 1 & - 1 & \lambda \end{matrix} \right| = 0 \Rightarrow \lambda^{3} + 3\lambda = 0$$ Therefore $\lambda = 0$, since $\lambda = i\sqrt{3}$does not exist.