A) 1, 2
B) \[1,-1\]
C) 1, 0
D) none of these
Correct Answer: B
Solution :
The given system of equations possess non-zero solutions. \[\therefore \] \[\left| \begin{matrix} 1 & 1 & 1 \\ 1 & a & a \\ 1 & -a & 1 \\ \end{matrix} \right|=0\] Applying \[{{R}_{2}}\to {{R}_{2}}-{{R}_{1}}\]and \[{{R}_{3}}\to {{R}_{3}}-{{R}_{1}}\] \[\Rightarrow \]\[\left| \begin{matrix} 1 & 1 & 1 \\ 0 & a-1 & a-1 \\ 0 & -a-1 & 0 \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[1\,[0-({{a}^{2}}-)]=0\] \[\Rightarrow \] \[{{a}^{2}}=1\] \[\Rightarrow \] \[a=\pm 1.\]
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