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3 and 4 .Determinants and Matrices
medium
સમીકરણની સંહતિ $\lambda x + y + z = 0,$ $ - x + \lambda y + z = 0,$ $ - x - y + \lambda z = 0$ ને શૂન્યતર ઉકેલ હોય, તો $\lambda $ ની કિમત મેળવો.
A
$0$
B
$1$
C
$3$
D
$\sqrt 3 $
(IIT-1984)
Solution
(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.
Standard 12
Mathematics
