| The set of all values of A, for which the system of linear equations |
| \[x-2y-2z=\lambda x\] |
| \[x+2y+z=\lambda y\] |
| \[-x-y=\lambda z\] |
A) is a singleton
B) contains exactly two elements
C) is an empty set
D) contains more than two elements
Correct Answer: A
Solution :
| \[\left| \begin{matrix} \lambda -1 & 2 & 2 \\ 1 & 2-\lambda & 1 \\ 1 & 1 & \lambda \\ \end{matrix} \right|=0\] |
| \[\Rightarrow \] \[\lambda -{{1}^{3}}=0\]\[\Rightarrow \] \[\lambda =1.\] |
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