| Find the value of c for which the following equations have non trivial solutions: |
| \[cx-y-z=0\] |
| \[-cx+y-cz=0\] |
| \[x+y-cz=0\] |
A) \[\frac{1}{2}\]
B) \[-1\]
C) \[2\]
D) \[0\]
Correct Answer: B
Solution :
| \[\left| \begin{matrix} C & -1 & -1 \\ -C & 1 & -C \\ 1 & 1 & -C \\ \end{matrix} \right|=0\]\[\Rightarrow \]\[\left| \begin{matrix} 0 & 0 & -(1+C) \\ -C & 1 & -C \\ 1 & 1 & -C \\ \end{matrix} \right|=0\]\[\Rightarrow \]\[-(1+C)(-C-1)=0\]\[\Rightarrow \]\[C=-1.\] |
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