The system of equations lambda x + y + z = 0, | vedclass

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Question

(a) Accordingly, $\left| {\,\begin{array}{*{20}{c}}\lambda &1&1\{ - 1}&\lambda &1\{ - 1}&{ - 1}&\lambda \end{array}\,} igh

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(a) Accordingly, $\left| {\,\begin{array}{*{20}{c}}\lambda &1&1\{ - 1}&\lambda &1\{ - 1}&{ - 1}&\lambda \end{array}\,} ight| = 0 \Rightarrow {\lambda ^3} + 3\lambda = 0$

Therefore $\lambda = 0$, since $\lambda = i\sqrt 3 $ does not exist.

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

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