A) for all real values of \[\lambda \]
B) only when \[\lambda =\pm \frac{1}{\sqrt{2}}\]
C) only when \[\lambda \ne 0\]
D) only when \[\lambda =0\]
Correct Answer: C
Solution :
Given matrix is non-singular , then \[\left| \begin{matrix} \lambda & 1 & 0 \\ 0 & 2 & 3 \\ 0 & 0 & \lambda \\ \end{matrix} \right|\ne 0\] \[\Rightarrow \] \[\lambda (2\lambda -0)\ne 0\] \[\Rightarrow \] \[\lambda \ne 0\]
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