The system of equations x + y + z = 0, - x + y + z = 0, - x - y +… - Vidyadip

MCQ

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

✓
$0$
B
$1$
C
$3$
D
$\sqrt 3 $

✓

Answer

Correct option: A.

$0$

a
(a) Accordingly, $\left| {\,\begin{array}{*{20}{c}}\lambda &1&1\\{ - 1}&\lambda &1\\{ - 1}&{ - 1}&\lambda \end{array}\,} \right| = 0 \Rightarrow {\lambda ^3} + 3\lambda = 0$

Therefore $\lambda = 0$, since $\lambda = i\sqrt 3 $ does not exist.

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